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ELEMENTS 

OF 



HEAT-POWER ENGINEERING 



BY 
C. F. HIRSHFELD, M.M.E. 

Professor of Power Engineering, Sibley College, Cornell University, Ithaca, N.Y. 



AND 



WM. N. BARNARD, M.E. 

Professor of Steam Engineering, Sibley College, Cornell University, Ithaca, N.Y. 



FIRST EDITION 

FIRST THOUSAND 



NEW YORK 

JOHN WILEY & SONS 

London: CHAPMAN & HALL, Limited 

1913 



t^J. 



5^ 



Copyright, 1912 

BY 

C. F. HIRSHFELD 

AND 



W. N. BARNARD 




Stanbope ipress 

F. H. GILSON COMPANY 
BOSTON, U.S.A. 



PREFACE 



In preparing this textbook the Authors have attempted to 
include in a single volume not only the elementary thermo- 
dynamic theory of gases and vapors and of their cycles, but also 
the consideration of the sources of heat, the methods of making 
it available for useful purposes, its utilization- in the various types 
of heat-driven prime movers and their auxiliary apparatus, 
together with a discussion of the fundamental theory, the ideal 
and actual performance and the practical considerations con- 
nected with such apparatus. The book is prepared primarily for 
the use of students in Mechanical Engineering in their junior 
and senior years, after they have completed college courses in 
physics, chemistry, analytical and applied mechanics and empir- 
ical machine design. The text is supposed to be supplemented by 
lectures, lantern slides, a study of trade catalogues and collateral 
reading; and, as it is prepared primarily for students who will 
have separate courses in mechanical laboratory practice and in 
the economic problems connected with heat-power engineering, 
but little relating to these branches is given. 

A large part of the material contained in the following pages 
has been used during the last four years, first in pamphlet 
and later in book form, as a text in the junior and senior courses 
in Sibley College, Cornell University. It has been revised from 
time to time as the necessity became apparent, and now the 
original matter has been practically rewritten, rearranged and 
considerably amplified for the present book. 

To add to its convenience and value as a textbook in recita- 
tion courses, all sections are numbered, the sub-paragraphs are 
lettered, and sample problems are given in the Appendix. 

Undoubtedly errors of various kinds will be discovered, and 
in order that they may be eliminated it is hoped that they will 
be brought to the attention of the Authors, who will also welcome 
any other suggestions for the improvement of the book. 



iv PREFACE 

The Authors express grateful acknowledgment of their in- 
debtedness to Professor A. W. Smith, Director of Sibley College, 
for many helpful suggestions and criticisms during the inception 
and progress of this work, and to Assistant Professor Ellenwood 
who prepared a large number of the appended problems. 

They desire to extend their thanks to Professor Lionel S. 
Marks and to Dr. Harvey N. Davis, and their publishers, 
Longmans, Green & Co., for permission to use an abstract of 
their steam tables, and to Professor Cecil H. Peabody and John 
Wiley and Sons for permission to use a reduced and modified 
drawing based on the former's temperature-entropy chart. 
Thanks are also due the following members of the Sibley Col- 
lege instructing staff for valuable assistance: Messrs. H. M. 
Parmley, T. C. Ulbricht, and R. Matthews; and to F. A. Burr, 
formerly Assistant Professor in the College. 



CONTENTS. 



PACK 

.1. Introductory xv 

CHAPTER I. — Heat i 

2. Heat a Form of Energy. 3. Unit of Heat Energy. 4. Solar Heat. 
5. Heat from Mechanical Energy. 6. Heat from Electrical Energy. 
7. Heat from Chemical Combination. 

CHAPTER II. — Elementary Laws of Heat Energy 6 

8. Conservation of Energy. 9. Ideal Mechanisms. 10. The Second 
Law of Thermodynamics. 11. Distribution of Associated Heat 
Energy. 12. Specific Heat. 13. Total Associated Heat. 

CHAPTER III. — The Heat-power Plant 16 

14. General. 15. The Steam-power Plant. 16. The Producer Gas- 
power Plant. 17. Analogy. 18. Further Study. 

CHAPTER IV. — The Laws of Gases 28 

19. States of Aggregation of Substances. 20. The Ideal Laws of Condi- 
tion of Gases. 21. The Specific Heats of Ideal Gases. 22. Constant- 
volume Specific Heat of Ideal Gas. 23. Constant-pressure Specific 
Heat. 24. The Ratio 7. 25. Table of Gas Constants. 

CHAPTER V. — Expansions and Compressions of Gases 43 

26. Volume Changes. 27. Isobaric Changes of Gases. 28. Isovolumic 
Changes of Gases. 29. Isothermal Changes of Gases. 30. Adia- 
batic Volume Changes of Gases. 31. General Expression for Volume 
Changes. 32. Construction of Lines Representing Volume Changes. 

CHAPTER VI. — Reversibility 59 

33. Definition. 34. Some Reversible Processes. 35. Some Irreversible 
Processes. 

CHAPTER VII. — Entropy 65 

36. Explanatory. 37. Definition. 38. Entropy Changes for Reversible 
Processes with Ideal Gases. 39. Sign of Entropy Changes during 
Reversible Processes. 40. Reversible Isobarics of Gases. 41. Revers- 
ible Isovolumics of Gases. 42. Reversible Isothermals of Gases. 
43. Reversible Adiabatics of Gases. 44. Irreversible Adiabatic Proc- 
esses of Ideal Gas, and the Corresponding Entropy Changes. 45. En- 
tropy Changes Independent of Path. 46. Temperature-entropy 
Diagrams. 

V 



Vi CONTENTS 

PAGB 

CHAPTER VIII. — Gas Cycles 76 

47. Definition of a Cycle. 48. Diagram of a Cycle. 49. The Carnot 
Cycle for Gases. 50. All Reversible Engines Have the Same Efficiency 
as the Carnot Engine. 51. Comparison of Carnot Engine and Real 
Engine. 52. T<^-Diagram of Carnot Cycle. 53. Criterion of Maxi- 
mum Efl&ciency. 54. The Constant-volume Regenerative or Stirling 
Cycle. 55. The Constant-pressure Regenerative, or Ericsson Cycle. 

56. Constant-volume Heat-change, Otto, or Beau de Rochas Cycle. 

57. Constant-pressure Heat-addition, Brayton, or Joule Cycle. 58. 
Diesel Cycle. 

CHAPTER IX. — Vapors 103 

59. Vapors and Gases. 60. Formation of Vapor. 61. Heat of the Liquid. 
62. Latent Heat of Vaporization. 63. Total Heat per Pound of 
Vapor. 64. Saturated Vapor. 65. Quahty 66. Superheated 
Vapor. 67. Heat per Pound of Superheated Vapor. 68. Diagram of 
Heat Changes during Vaporization. 69. Vapor Tables. 70. Satura- 
ation Curve. 71. Defining Conditions for Saturated Vapors. 
72. Evaporation. 73. Boihng. 74. Temperature-entropy Changes 
of Vapors. 75. Continuity of the Liquid and Gaseous States. 
76. Van der Waals' Equation for Real Gases. 

CHAPTER X. — Properties of Steam 126 

77. Steam or Water Vapor. 78. Sources of Data. 79. Properties of 
Dry Saturated Steam. 80. Properties of Superheated Steam. 
81. Temperature-entropy Chart for Water and Steam. 82. The 
Mollier Chart, or Q0-Chart. 

CHAPTER XL — Volume Changes of Vapors 146 

83. General. 84. Constant-pressure and Isothermal Volume Changes for 
Saturated Vapors. 85. Constant-pressure Volume Changes of Super- 
heated Vapors. 86. Isothermal Volume Changes of Superheated 
Vapors. 87. Adiabatic Changes of Saturated Vapors. 88. Adiabatic 
Changes of Superheated Vapors. 89. Constant-volume Changes of 
Saturated Vapors. 90. Constant- volume Changes of Superheated 
Vapors. 

CHAPTER XII. — Vapor Cycles 161 

91. Carnot Cycle with Dry Saturated Steam. .92. The Carnot Cycle 
with Any Vapor. 93. Clausius Cycle with Dry Saturated Water 
Vapor. 94. The Clausius Cycle in General. 95. The Rankine Cycle. 
96. The Rankine Cycle in General. 97. Cycle with Rectangular PV- 
diagram. 98. The Rectangular PV-cycle in General. 

CHAPTER XIII. — Power, Efficiency, and Performance 180 

99. Power. 100. Distinction between Real and Ideal Engines. loi. The 
Indicator. 102. The Indicator Diagram. 103. Methods of Deter- 
mining the Area of an Indicator Diagram. 104. Delivered Power. 
105. Efi&ciencies. 106. Engine Performance. 



CONTENTS Vij 

PAGE 

CHAPTER XIV. — The Theoretical Steam Engine 194 

107. General. 108. The Carnot Cycle and the Steam Engine. 109. The 
Regenerative Steam-engine Cycle. no. The Clausius Cycle. 
III. The Rankine Cycle. 112. Clearance and Compression. 113. 
Cushion Steam and CyUnder Feed. 114. Saturation and Quality 
Curves. 

CHAPTER XV. — Action of Steam in Real Engines 208 

115. Cylinder and Thermal Efficiencies of the Steam Engme. 116. Act- 
ual Behavior of Steam in an Engine Cylinder. 117. Diagrammatic 
Representation of the Heat Interchange in the Cylinder. 118. Deriv- 
ation of a T<^-diagram from a PV-diagram. 119. Hirn's Analysis. 
120. Experimental Determination of the Actual Performance of Steam 
Engines. 121. Steam Calorimeters. 122. Weight of Steam Ac- 
counted for by the Indicator Diagram. 

CHAPTER XVI. — Methods of Decreasing Cylinder Condensation. 230 
123. Condensation and Leakage. 124. Size and Proportions of Cylinder. 
125. Influence of Point of Cut-off. 126. Compounding of Cylinders. 
127. Gain Due to Condensing the Exhaust Steam. 128. Effect of 
Superheated Steam. 129. Use of Steam Jackets. ' 130. Reheating 
Receivers. 131. Other Methods of Reducing Cyhnder Condensation. 

CHAPTER XVII. — Steam Engines 244 

132. Steam-engine Parts. 133. Classification and Types of Steam Engines. 

CHAPTER XVIII. — Steam-engine Governors 255 

134. Governing. 135. Governing of Steam Engines. 136. Governors. 
137. Pendulum Governors. 138. Spring-balanced Fly-ball Governor. 
139. Elementary Shaft Governors. 140. Commercial Types of Shaft 
Governors. 

CHAPTER XIX. —The Valve Gears of Steam Engines 271 

141. Introduction. 142. The Engine — Definitions. 143. The Valve — 
Definitions. 144. Action of the D-valve and Eccentric. 145. Rela- 
tive Valve and Piston Positions. 146. Elliptical Diagram. 147. The 
Sweet Diagram. 148. Zeuner Diagram. 149. Bilgram Diagram. 
150. Distortion Due to Angularity of the Connecting Rod. 151. Valve 
Diagrams Considering "Angularity" of the Connecting Rod. 152. 
Valve and Port Openings. 153. Cushioning the Reciprocating Parts. 
154. Early Valve Opening. 155. Limitations of the Simple Valve. 
156. Special Types of Single Valves. 157. Valve Gears for High- 
speed Engines. 158. General Characteristics of Independent Cut-off 
Gears. 159. Independent Cut-off Valve with Stationary Seat. 
t6o. Riding Cut-off Valves. 161. Gears with Oscillating Valves. 
162. Link Gears. 163. Radial Valve Gears. 164. Poppet Valves 
and Their Gears. 



VUl CONTENTS 

PAGB 

CHAPTER XX. — Conventional Indicator Diagram 323. 

165. Conventional Diagram for Simple Engines. 166. Diagrams for Mul- 
tiple-expansion Engines. 167. Diagrams of Woolf Type of Engine. 
168. Diagrams for Engines with Infinite Receivers and No Clearance 
(General). 169. Receiver Pressures in Compound Engines. 170. 
Cylinder and Expansion Ratios Used in Multiple-expansion Engines. 
171. The Theoretical Indicator Diagrams of Multiple-expansion 
Engines with Clearance. 172. Effects of Changing the Cut-offs in the 
Respective Cylinders of Multiple-expansion Engines. 173. Theoreti- 
cal PV-diagrams of a Tandem Compound Engine. 174. Theoretical 
PV-diagrams of a Cross Compound Engine. 175. Theoretical PV- 
diagrams of Multiple-expansion Engines (General Case). 176. The 
Actual Combined Indicator Diagrams of Multiple-expansion Engines. 



35* 



CHAPTER XXI. — Performance of Steam Engines 

177. Steam Consumption. 178. Steam-engine Performance (Data). 

CHAPTER XXII. — Steam Turbines 359, 

179. Introductory. 180, Thermodynamics of the Ideal Steam Turbine. 
181. Thermodynamics of Actual Turbines. 182. The Dynamics of 
Impulse Steam Turbines. 183. De Laval Type of Single-Stage Tur- 
bine. 184. Pelton Type of Steam Turbine. 185. Rateau Type of 
Steam Turbine. 186. Curtis Type of Steam Turbine. 187. Veloc- 
ity Compounding with a Single Row of Rotating Buckets. 188. Re- 
action Turbines. 189. Applications of the Steam Turbine. 190. 
Advantages and Disadvantages of the Steam Turbine. 191. Steam 
Turbine Performance. 

CHAPTER XXIII. — External Combustion Gas Engines 397 

192. Definition. 193. The Hot-Air Engine. 194. Rider Hot-Air En- 
gine. 195. Ericsson Hot-Air Engine. 

CHAPTER XXIV. — Internal Combustion Engines. Methods of 

Operation 403. 

196. Advantages and Types. 197. Cylinder Operations of Four-Stroke 
Otto Cycle. 198. The Air Card. 199. Real Indicator Card for 
Four-Stroke Cycle. 200. Losses in the Four-Stroke-Cycle Engine. 
201. Requirements for High Efficiency of Combustion. 202. Indi- 
cated Work and Power of the Four-Stroke-Cycle Engine. 203. The 
Two-Stroke-Cycle Otto Engine. 204. The Diesel Engine. 205. 
Modifications to Suit Different Fuels. 206. Compression and Maxi- 
mum Pressures. 

CHAPTER XXV. — Internal Combustion Engines. Mechanical 

Features 420. 

207. Cylinder Arrangement. 208. Classification. 209. Methods of 
Producing Combustible Mixtures. 210. Carburetors. 211. Treat- 
ment of Heavy Oils. 212. Methods of Governing Internal-Combus- 



CONTENTS IX 

PAGE 

tion Engines. 213. Gas Valves, Mixing Valves, etc. 214. Methods 

of Ignition. 215. Hot-Tube Ignition. 216. Spontaneous Ignition. 

217. Electric Ignition. 218. Internal-Combustion Engine Valve 
Gear. 

CHAPTER XXVI. — Internal-Combustion Engines. Efficiency, 

Performance and Power 443 

219. Efficiencies of Otto Four-Stroke-Cycle Engine. 220. Efficiencies of 
Otto Four-Stroke-Cycle Engines. 221. Heat Balance for Gas En- 
gines. 222. Performance of Internal-Combustion Engines. 

CHAPTER XXVII. — Fuels 455 

223. Fuels. 224. Geology of Coal. 225. Composition of Coal. 226. 
Coal Analyses. 227. Fuel Values of Coals. 228. Coke. 229. 
Wood. 230. Municipal and Industrial Waste. 231. Natural Oil and 
Its Products. 232. Alcohol. 233. Natm-al Gas. 234. Artificial 
Gases. 

CHAPTER XXVIII. — Combustion 472 

235. Definitions. 236. Combustion of Carbon. 237. Weights of Oxy- 
gen and Air Necessary for Combustion of Carbon. 238. Volumes of 
Gases Involved in Combustion of Carbon. 239. Temperature of 
Combustion. 240. Combustion of Hydrogen. 241. Hydrocarbons. 
242. Combustion of Sulphur. 243. Combustion of Mixture of Ele- 
ments. 244. Fuel Calorimeters and Heat Value. 245. Flue Gas 
Analysis. 246. Weight of Flue Gases. 247. Percentage of Excess 
Air. 248. Stack Losses. 

CHAPTER XXIX. — Actual Combustion of Fuels — Furnaces and 

Stokers — Oil Burners 503 

249. Introductory. 250. Air Supply. 251. Conditions for Complete 
and Smokeless Combustion. 252. Value of Coal as Furnace Fuel. 
253. Burning Powdered Coal. 254. Selection and Purchase of Coal. 
255. Furnace Operation. 256. Grates and Furnaces. 257. Auto- 
matic Mechanical Stokers. 258. Burning Liquid Fuel. 

CHAPTER XXX. — Boilers 533 

259. Losses Connected with Steam Generation. 260. Efficiencies Con- 
nected with Steam Generation. 261. Boiler Heating Surface and 
Heat Transmission. 262. Boiler Explosions. 263. Selection of 
Boilers. 264. Classification of Boilers. 265. Internally Fired Tu- 
bular Boilers. 266. Externally Fired Tubular Boilers. 267. Water 
Tube Boilers. 268, Boiler Accessories. 269. Boiler Performance. 
270, Proportioning the Boiler for Power Output. 

CHAPTER XXXI. — Superheaters 565 

271, Advantages of Superheating. 272. Types of Superheaters. 273. 
Separately Fired Superheaters. 274. Boiler Draft Superheaters. 
275. Protection of Superheater. 276. Superheater Surface. 



X CONTENTS 

CHAPTER XXXII. — Draft and Drapt Apparatus ^^74 

277. General Principles. 278. Amount of Pressure Drop Required. 
279. Chimney Draft. 280. Artificial Draft. 

CHAPTER XXXIII. — Gas Producers and Producer Gas 590 

281. Essentials of Producer-Gas Apparatus. 282. Simple Theory of Pro- 
ducer Action. 283. Efficiency, Simple Producer Action. 284. More 
Advanced Theory of Producer Action. 285. Practical Limitations. 
286. Artificial Cooling of Producers (General). 287. The "Carbon 
Monoxide" Method of Temperature Control. 288. The Water Vapor 
Method of Temperature Control. 289. Eflfects of Hydrocarbons in 
Fuels. 290. Water Bottom and Grate Bottom Producers. 291. 
Induced Draft and Forced Draft. 292. Mechanical Charging. 293. 
Cleaning Apparatus. 294. Producer Gas from Oil. 

CHAPTER XXXIV. — Utilization of Waste Heat — Financial Con- 
siderations 619 

295. General. 296. Utilization of the Heat in the Flue Gases. 297. 
Utilization of the Heat in the Exhaust Steam. 298. Heat Transmis- 
sion. 299. Financial Considerations. 

CHAPTER XXXV. — Heat Transfer 624 

300. General. 301. Heat Conduction. 302. Heat Transfer by Convec- 
tion. 303. Heat Transfer by Radiation. 304. Heat Transfer by 
Engineering Apparatus. 305. Effectiveness of Heat Transmitting 
Surfaces. 306. Cases of Heat Transmission through Plates. 307. • 
Case I. (r = Const.) A Hot Substance at Constant Temperature 
Surrenders Heat to a Cold Fluid which Flows. 308. Case II. {t = 
Const.) A Substance at Constant Temperature {t) Receives Heat 
from Another Flowing Substance whose Temperature Decreases. 
309. Case III. Parallel Flow in the Same Direction. 310. Case 
IV. Counterflow. 311. Case V. {T = const, and t = const.) A 
Hot Substance Surrenders Heat at Constant Temperature to a Cold 
Substance whose Temperature is Constant. 

CHAPTER XXXVI. — Apparatus for Heating Feed Water 651 

312. Object of Heating Feed Water. 313. Feed-Water Heaters in Gen- 
eral. 314. Open Heaters. 315. Closed Heaters. 316. Econo- 
mizers. 

CHAPTER XXXVII. — Condensers and Related Apparatus 664 

317. Advisability of Condensing. 318. Condensers in General. 319. 
Contact Condensers. 320. Surface Condensers. 321. Air Pumps. 
322. Recovery of Condensing Water. 

CHAPTER XXXVIII. — Water Purification 685 

323. Impurities in Natural Waters. 324. Troubles from Untreated Feed 
Water, 325, Methods of Treating Feed Waters. 



CONTENTS Xi 

PAGE 

CHAPTER XXXIX. — Power Plants 690 

326. General. 327. Internal Combustion Engine Plants. 328. Steam 
Power Plants. 

CHAPTER XL. — Continuous Flow of Gases and Vapors through 

Ortfices and Nozzles 698 

329. Introductory. 330. Flow of Saturated Steam in the Ideal Case. 
331. The Ideal Steam Nozzle. 332. Actual Steam Nozzles, t,;^^. 
Empirical Formulas for the Flow of Steam through Orifices. 334. 
Flow of Steam through Pipes. 335. AppUcation of Steam Nozzles. 
336. Perfect Flow of Ideal Gases. 337. Imperfect Flow of Gases. 

CHAPTER XLI. — Compressed Air 716 

338. Definitions. 339. Elementary Air Compressor. 340. Work Done 
in Compressor. 341. The Effect of Clearance. 342. Real Single 
Stage Compressor Diagram. 343. Volumetric Efficiency. 344. 
Cooling During Compression. 345. Blowing Engines. 346. Tur- 
bine Compressors. 347. Compressed Air Engines. 348. Com- 
pressed Air Engine Cycles. 349. Preheating. 

CHAPTER XLII. — Refrigeration 734 

350. Definition. 351. Thermodynamics of Refrigeration. 352. The Air 
Refrigerating Machine. 353. Vapor Compression Process of Refrig- 
eration. 354. Relative Advantages of Different Vapors. 355. The 
Ammonia Absorption Process. 356. Rating of Refrigerating Ma- 
chines. 

PROBLEMS 749 

APPENDIX 780 

TABLES xiii 



TABLES. 



TABLE PAGE 

I . — Gas Constants 40 

II. — Collected P, V, T, Formulas for Volume Changes of Gases. . 58 

III. — Gas Cycles 102 

IV. — Usual Gage Pressures 241 

v.— (i +\oger) ^r 325 

VI. — Diagram Factors 325 

VII. — Summary of Performances of Steam Engines 355 

VI 11. — Summaries of Efficiencies of Steam Engines 358 

IX. — Steam Consumptions of Steam Engines 358 

X. — Steam-Turbine Performance 395 

XI. — Common Compression Pressures 419 

XII. — Efficiencies of Otto Four-Stroke Cycle Engines 443 

XIII. — Old Classification of Coals , 457 

XIV. — Parr's Classification of Coals (Abbrev.) 458 

XV. — Ultimate Analyses of Coals 460 

XVI. — Commercial Sizes of Soft Coal 465 

XVII. — Sizes of Anthracite Coal , 466 

XVIII. — Typical Analyses of Natural Gas 470 

XIX. — Combustion Data 473 

XX. — Properties of Air 477 

XXI. — Flue Gas Constants 479 

XXII. — Flue Gas Constants 481 

XXIII. — Calorific Values of Hydrocarbons 491 

XXIV. — Pressure Drops through Boilers 578 

XXV. — Typical Analyses of Producer Gases 602 

XXVI. — Specific Conductivity of Various Materials 628 



INTRODUCTORY. 



I. The advancement of the human race has been largely due 
to the fact that man has greater ability than his fellow creatures 
to utilize nature's resources. At first he was driven by his own 
weakness to seek nature's aid for protection, and he thus became 
familiar with her simpler laws. This knowledge grew steadily 
and after a time was recorded. Now the accumulated informa- 
tion is too great to be grasped by any individual or group and it 
has become necessary to specialize. One group of specialists, the 
scientists, continue to delve after nature's secrets in order to add 
to the store of human knowledge; another group, the engineers, 
work to make application of discovered laws to meet the needs 
of humanity. 

The engineer must know nature's laws and must be familiar 
with their applications in order that he may be able to aid the 
race in the development and improvement of its life. One of the 
most important of his problems results from the fact that man's 
body cannot supply the power required to carry out the con- 
ceptions of his mind. To solve this problem the engineer draws 
on nature's store of energy. 

In general, the energy of nature's store is not directly available 
for human uses; it must be changed in kind or quality, trans- 
mitted through space, and made available at times of demand. 
The engineer must provide means for effecting these results. 

One of the best examples of such changes is furnished by the 
conversion of heat energy into the mechanical form by means of 
Heat Engines. Since the world demands enormous supplies of 
mechanical energy, this sort of conversion is of great impor- 
tance, because of the fact that immense stores of easily trans- 
portable fuel are distributed over the earth near its surface. 
This fuel has latent heat energy, which may be easily converted 
into available heat energy by con>bustion. It is then the duty 
of the heat engine to convert as large a part as possible of this 



XVI INTRODUCTORY 

available heat energy into the more desirable form of mechanical 
energy. 

The following pages are devoted to a consideration of trans- 
formations of latent heat in fuel into available heat, and of avail- 
able heat into mechanical energy, together with a study of the 
devices by which the transformations are effected. 

The theory of these transformations is called Thermodynamics, 
while the whole subject, theoretical and practical, may be called 
Heat-Power Engineering. 



HEAT-POWER ENGINEERING. 



CHAPTER I. 

HEAT. 

2. Heat a Form of Energy. It has been shown experimentally 
that heat can be produced by the expenditure of other forms 
of energy, and that other forms of energy can be produced 
by the expenditure of heat. Therefore the conclusion that heat 
is a form of energy is justified. 

All bodies that man knows possess heat energy, " associated 
heat"; whatever the material or state of a body may be, it is 
possible to obtain heat energy from it. It is not known how this 
heat energy is stored in matter, but it is certainly possible, and 
it seems probable, that it is in some way associated with the 
motions and relative positions of the constituent particles. Be- 
yond this it is not necessary to generalize here in the present state 
of knowledge. 

3. Unit of Heat Energy. The unit of measurement of 
energy is based upon some effect produced by the kind of energy 
to be measured. Under certain conditions a rise in temperature 
of a body is one of the most obvious phenomena connected with 
an increase of associated heat; and, as the extent of this elTect 
may be measured, it is used as the basis of the unit of heat 
energy. 

In English-speaking countries the unit of heat energy is 
known as the British Thermal Unit (B.t.u.) and is defined as 
follows : 

The British Thermal Unit is the quantity of heat required to 
raise the temperature of one pound of pure water one Fahrenheit 
degree. 

When extreme accuracy is desired it is necessary to specify 
the point on the temperature scale at which the one-degree rise 



2 HEAT-POWER ENGINEERING 

takes place, as it requires slightly different amounts of heat at 
different temperatures. This temperature is usually taken either 
at 39.1° F., at which water has maximum density, or at 62° F.* 

For ordinary engineering purposes, however, it is customary 
and sufficiently accurate to consider the heat corresponding to 
one-degree rise as constant throughout the scale. Hence the 
definition given serves for the engineer. 

What has been termed a " mean B.t.u." is also used. It is 
defined as xioth of the heat required to raise the temperature of 
one pound of pure water from 32° to 212° F. The difference 
between this mean B.t.u. and the one defined is negligible in 
most engineering computations. 

Sources of Heat. 

4. Solar Heat. Heat for human use probably all comes, 
directly or indirectly, from the sun. This heat is applied 
directly to produce a sufficiently high temperature on portions 
of the earth's surface to render plant growth and animal life 
possible. 

Heat engines have been built which convert heat derived 
directly from the sun into mechanical energy ; but, because their 
bulk is great in proportion to the energy transformed, and be- 
cause the sun's rays are not always available when needed, 
they have not as yet been commercially successful. 

The energy of the sun's rays is applied indirectly through the 
agency of plant growth and geologic processes to produce stores 
of fuel in the earth's crust. Heat energy, indirectly from the 
sun, may be evolved for human use from this fuel. 

Also the sun's rays falling upon water surfaces cause evapora- 
tion whereby heat is converted into mechanical energy. This 
energy lifts the water vapor, which is again condensed and falls 
upon the earth's surface as rain or snow. The resulting water 
flowing to its original level prepares the soil for plant growth; 
it irrigates plants and turns water wheels to supply mechanical 
energy. 

Heat may be derived from mechanical energy, electrical energy, 
or from the chemical combination of certain elements. In most 
cases the ultimate source of the energy is probably the sun. 

* The value 59° F., corresponding to the scientist's 15° C, is sometimes used. 



HEAT 3 

5. Heat from Mechanical Energy. Primitive man generated 
heat to kindle fires by rubbing two sticks together. The me- 
chanical energy due to the muscular effort that moves the 
sticks reappears as heat. This heat is derived indirectly from 
the sun, since the sun's energy makes possible animal life and 
therefore muscular effort. 

The engineer is familiar with the production of heat by machine 
friction. This again is a case of conversion of mechanical 
energy (indirectly from the sun) into heat. This is an unde- 
sirable conversion, since mechanical energy, which should be 
available for useful purposes, becomes useless heat. The same 
change occurs when a machine is retarded or stopped by a fric- 
tion brake. This is a useful change, however, since mechanical! 
energy, which cannot be used and which may become dangerous, 
is dissipated as heat and rendered harmless. 

In general, heat for human use is not derived from mechanical 
energy because it may be obtained in other ways more con- 
veniently and at less cost. 

6. Heat from Electrical Energy. The conversion of elec- 
trical energy into heat is illustrated by every electric conductor 
that carries a current; for, though the reason is unknown, heat 
results whenever an electric current flows. This is known 
to the electrician as the PRAoss. It is always a loss if the 
delivery of maximum electrical energy is the object of the flow; 
but it would not be a loss if heat were the object, as in electric 
furnaces and stoves. Except for special service electrical energy 
is too expensive a source of heat. 

7. Heat from Chemical Combination. There is almost 
always a liberation of heat when substances combine chemically. 
In general, the more violent the reaction and the more stable the 
compound formed, the greater the amount of heat liberated. 
There are a few combinations which are accompanied by heat 
absorption; but the compounds formed are generally quite 
unstable at ordinary pressures and temperatures and the heat 
absorbed is usually quite small. 

The physical chemist briefly explains the phenomenon of heat 
evolution during chemical combination by saying that chemical 
energy is converted into heat energy. It is well, however, to 



4 HEAT-POWER ENGINEERING 

understand his more exact expression, which is at times useful 
to the engineer. 

In every chemical system, or group of systems, there is a cer- 
tain total amount of " intrinsic " energy. This amount depends 
upon the kind of system and upon the physical condition. If 
several such systems react to form new systems, the latter may 
have a different total quantity of intrinsic energy from the former. 
If the intrinsic energy of the new system is less than that of the 
other, energy must have been liberated; if greater, energy must 
have been absorbed. Energy thus liberated may appear in one 
or all of its forms; but the largest part of it usually appears as 
heat. 

Thus to supply heat by chemical combination it is necessary 
to utilize systems that can react to form new systems with less 
total intrinsic energy. 

To illustrate, consider the production of heat by the combina- 
tion of carbon and oxygen to form carbon dioxide. The total 
intrinsic energy of the system of carbon molecules and of the 
system of oxygen molecules is greater than the intrinsic energy 
of the resulting system of carbon-dioxide molecules. This dif- 
ference is the source of most of the heat energy used by the 
engineer. 

It is convenient when dealing with these changes to refer to 
gaseous materials as standards, since the laws of gases are sim- 
plest. If a unit weight of gaseous carbon could be combined with 
gaseous oxygen at some standard temperature and pressure to 
form gaseous carbon dioxide, a certain amount of energy would 
be liberated. If some or all of this energy appeared as heat, and 
if the reacting substances were insulated so that no heat could 
leave the system, the resulting carbon dioxide would be raised 
to a high temperature and possibly to a high pressure. Then if 
heat were withdrawn until the original temperature and pressure 
were reached, the heat removed might be called the standard 
heat quantity due to this reaction. Gaseous carbon, however, 
cannot be used in these operations, only the solid forms being 
available. Experience and experiment show that to change a 
solid to a liquid or a gas requires an expenditure of heat. In 
the chemical combination just referred to, heat is absorbed to 
change solid carbon to gaseous carbon, so that the heat liberated 
is less than if gaseous carbon had been used; that is, the heat 



HEAT 5 

liberated is less than that which has been called the standard 
quantity. Similarly, if the product of the reaction were liquid 
or solid at ordinary temperatures, instead of a gas, the heat 
withdrawn to condense to the liquid or solid form would be added 
to the standard quantity. 

There will be further discussion of these phenomena under the 
head of combustion. They are mentioned here to indicate the 
nature of the engineer's problem of heat generation. 



CHAPTER II. 

ELEMENTARY LAWS OF HEAT ENERGY. 

8. Conservation of Energy, (a) It seems to be one of nature's 
great universal laws that energy cannot be created or destroyed. 
Experience and experiment have tended to establish this law, 
and now there is no reason to doubt that it holds throughout 
the universe. This Law of Conservation of Energy may be 
stated as follows: Energy cannot he created or destroyed; but all 
forms of energy are mutually interconvertible. 

Unfortunately, the engineer has adopted no unit for the meas- 
urement of quantities of energy that is common to all its forms. 
Each kind of energy is measured in its own unit of quantity, 
and each unit was originally fixed independently, because of 
convenience of measurement. The necessity for conversion of 
units of one form of energy into the units of another form was 
disregarded ; as a result the constant for conversion is sometimes 
inconvenient for use. Thus, for example, the unit of mechanical 
energy, the foot-pound, is about yis of the unit of heat, the 
British thermal unit; while the unit of electrical energy, the 
joule, is equal to 0.7373 foot-pounds. 

The engineer who deals with heat engines is chiefly concerned 
with the interconversion of units of heat and units of mechanical 
energy; he must constantly use the corresponding conversion 
factor. The determination of this factor requires very accurate 
experimentation with very delicate apparatus, and the most care- 
ful determinations yet made leave some uncertainty as to the 
exact value. Pending more exact knowledge, engineers com- 
monly use the value 778. 

(b) The Law of Conservation of Energy, when limited to 
heat and mechanical energy, is called the First Law of Thermo- 
dynamics, and it may be stated thus: 

Heat and mechanical energy are indestructible and interconvertible. 
The relation of units is 

1 B.t.u. = 778 foot-pounds. 



ELEMENTARY LAWS OF HEAT ENERGY 7 

In heat engines all of the energy supplied as heat does not 
appear as mechanical energy. This is not because heat energy 
is destroyed, but because part of it escapes conversion and leaves 
the engine still in the form of heat. However, each B.t.u. that 
is converted is transformed into 778 foot-pounds of work. 

(c) In order to do mechanical work there must be motion, and 
in all real cases the motion meets with resistance of some form. 
Anything that resists motion takes away energy; thus, friction 
might take away heat; a belt might take away mechanical energy; 
a metallic circuit might take away electrical energy; if the 
motion produces sound, energy is taken away as sound waves in 
the air. If any energy whatever were taken away, that is, if there 
were any resistance, and the machine continued in motion without 
continued energy supply, it would have to give out energy that 
it did not receive. 

It is, of course, impossible to conceive of, or build, a machine 
which will create energy. Such a machine would give one 
type of " perpetual motion." To distinguish this type, in 
which energy is created, from the others to be considered later, 
it will be called Perpetual Motion of the First Type. 

It follows directly, from the law of conservation of energy, 
that Perpetual Motion of the First Type is impossible. It is 
also apparent that the First Law of Thermodynamics is a special 
case falling under this broad general statement. 

9. Ideal Mechanisms. In the discussion of some engineering 
problems it is customary to assume ideal mechanisms for pur- 
poses of comparison. There are three types of Perpetual Motion 
used in discussing these. The first has just been considered; 
that commonly termed the " Second Type" will be more easily 
understood later in the discussion. The Third Type of Per- 
petual Motion is that most commonly assumed for purposes of 
analysis of mechanical problems. It is the ideal perpetual 
motion of a frictionless machine, which, once started, would 
continue in motion forever unless stopped' by some external 
resistance or force. 

As a matter of fact, no real machine can be frictionless, and 
therefore no real machine could continue in motion indefinitely; 
but the friction losses in machines can be reduced to almost 
negligible values, and for the purpose of analysis this may be 



HEAT-POWER ENGINEERING 



assumed to be carried to the limit, giving perpetual motion of 
the third type as an ideal possibility. 

10. The Second Law of Thermodynamics, (a) It is a matter 
of common observation that in a steam engine, for instance, the 
steam exhausted still contains a considerable quantity of heat, 
and that its temperature is lower than that of the steam supplied 
to the engine. 

This phenomenon of receiving heat at a high temperature 
and rejecting some of it at a lower temperature is characteristic 

of every real engine, and will 
be shown later to be charac- 
teristic of every ideal engine, 
no matter how perfect. The 
operation of all such engines is 
pictured graphically in Fig. i. 
Heat energy at the high tem- 
perature Ti flows from reser- 
voir / into the engine. There 
part of it is converted into the 
stream of mechanical energy 
(shown flowing out to the 
right), while the rest passes 
completely through the engine 
and -emerges, still in the form 
of heat, but at the lower tem- 
perature T2 of heat receiver //, which absorbs it. 

Calling the heat supplied in a given time Qi, the mechanical 
energy leaving W, and the heat leaving Q2, it follows from the 
conservation of energy that 

W-hQ2 = Qi. 
This rearranged gives 

W ^Qi- Q2, 

from which it immediately appears that the smaller Q2 is the 
greater will be the work resulting from the use of a given quantity 
of heat Qi. 

(b) Experience has shown that no device can even be imagined 
which, under existing circumstances, could continuously convert 
into mechanical form all of the heat energy supplied it. All 
machines so far devised, actual or ideal, can continuously convert 




Fig. I 



■Diagrammatic Representation 
of ■ a Heat Engine. 



ELEMENTARY LAWS OF HEAT ENERGY g 

only part of the heat suppUed them and must reject the remainder 
at a lower temperature than that at which it was received. This 
is summed up in the so-called Second Law of Thermodynamics 
as follows: 

No machine, actual or ideal, can both completely and continu- 
ously transform heat into mechanical energy."^ 

(c) If such complete transformation could be effected, it would 
give what is called Perpetual Motion of the Second Type. 

So long as heat must be exhausted at a lower temperature 
the possibility of obtaining mechanical energy from heat ceases 
as soon as the temperature of all the heat in the universe has 
been dropped to the lowest attainable value. 

If this necessity of exhausting heat at a lower temperature 
were removed, it would be possible to continue the conversion 
of heat into mechanical energy after all means of obtaining a 
temperature difference had been used up, that is, after all heat 
had been reduced to the lowest attainable temperature. 

As all mechanical energy eventually passes back into heat 
energy (generally at low temperature) through friction and 
allied phenomena, there would be no danger of the supply of 
heat giving out. The cycle would then be an endless one, con- 
sisting of the transformation of heat into mechanical energy, 
the retrogression from this form of energy to heat, the conversion 
to mechanical form again, and so on ad infinitum. 

This would then be equivalent to a sort of perpetual motion 
which is distinguished from the other two types by calling it, as 
above, Perpetual Motion of the Second Type. Hence the Second 
Law of Thermodynamics may also be stated thus: 

Perpetual Motion of the Second Type is impossible. 

This Second Type of Perpetual Motion, like the First Type, is 
impossible even in imagination, whereas the Third Type, though 
impossible of realization, is an ideal limit of possibilities. 

II. Distribution of Associated Heat Energy, (a) Common ex- 
perience shows that the quantity of heat associated with any por- 
tion of matter may be changed and that the transformation is 
accompanied by other definite phenomena such as change of 

* There are almost as many statements of the Second Law as there are authors 
of books on thermodynamics. It is beUeved that the statement as here given is the 
most satisfactory for the purposes of this book. 



lO HEAT-POWER ENGINEERING 

pressure, or of volume, or of temperature, or of physical state; 
chemical change may also occur and other forms of energy may 
appear or disappear. 

Despite these varied possibilities a very simple and definite 
generalization may be made. This at least serves the purpose 
of establishing a viewpoint and aids in analysis. 

Consider, for example, a single chemical substance, which 
may be an element or a compound, and which is assumed not 
to be set in motion as a whole, nor to he altered chemically, nor to 
lose energy by any form of radiation. In such a substance there 
can be only three results from adding heat, and there are only 
three sources from which heat can be abstracted. 

1. Heat addition may be accompanied by rise in temperature. 
In this case that part of the heat which is used in causing the 
temperature change may be conceived as effecting an increase 
in the motion of the constituent particles. Heat thus used is 
known as Sensible Heat and its addition increases the substance's 
store of sensible heat. Conversely, the abstraction of heat may 
be accompanied by a fall in temperature (probably decrease 
of internal motion) , and the source of part of the abstracted heat 
is the store of sensible heat of the substance. 

2. Heat addition may be accompanied by a variation of the 
internal structure of the substance, and this may be imagined as 
a molecular rearrangement. The part of the heat which is used in 
causing this change is called Internal Latent Heat. Conversely, 
the abstraction of heat may cause the reverse change. 

3. In I and 2 when heat is added the size of the substance may 
change ; there would then be a positive or negative displacement of 
surroimding media, against resistance, and part of the heat added 
supplies the necessary mechanical energy for this displacement. 
The heat thus transformed is sometimes called External Latent 
Heat. Conversely, when heat is abstracted in i and 2 the sur- 
rounding media may return and the equivalent of the external 
latent heat be abstracted as heat. 

(b) Heat energy added may then be imagined to produce 
results as follows: 

In I, part of the added heat may increase the kinetic energy of 
the molecules. 

In 2, part of the added heat may overcome the resistance to re- 
arrangement of the molecules. 



ELEMENTARY LAWS OF HEAT ENERGY II 

In 3, part of the added heat may overcome the resistance of 
surrounding media to displacement. 

In all cases the added heat becomes stored energy; for if the 
phenomena are reversed (conduction and radiation loss being 
prevented) the substance will return to its original dimensions, 
state, and temperature, and the energy previously given to the 
substance to accomplish these results will be returned as heat. 
Since the sensible heat and the internal latent heat are stored 
within the substance itself, and since the external latent heat is 
stored in external media, it is common to call the sum of the first 
two the Change of Intrinsic Heat Energy and the third the Change 
of External Heat Energy. 

(c) The following symbols will be used to designate, in thermal 
units, the various quantities concerned in changes of associated 
heat energy in substances : 

A(2 = the total quantity of heat added to or taken from the 

substance. 
A^ = the part of A(2 associated with temperature change; 

this equals the change of sensible heat. 
AJ = the part of A(2 associated with internal rearrangement; 

this equals the change of internal latent heat. 
A£ = the part of A(2 associated with the displacement of 
external media; this equals the change of external 
latent heat. 
From the foregoing discussion it follows that: 

A(3 = A5 + A/ + AE, (i) 

for the three symbols on the right of the equation represent the 
only destinations possible for added heat, and the only possible 
sources of abstracted heat. 

Thus the change of intrinsic heat energy = A^ + A/, the 
change of external heat energy = A£ and the change of total 
associated heat energy = AQ = A^" + A/ + AE. 

It is in general possible for any or all of the three terms on 
the right of the last equation to be either positive or negative or 
equal to zero. Hence it is necessary, within the conditions set 
at the beginning, to consider the equation as perfectly general, 
and to interpret it for the conditions of each case. 

(d) As an illustration of the foregoing statements, consider 
the transformations that occur and the heat that is utilized 



HEAT-POWER ENGINEERING 



H 



•; (Ox M> 

o 




Fig. 2. 



in generating steam from cold water. In the cylinder, above 
burner a in Fig. 2, let there be cold water, say at room temper- 
^ ature, below the piston. Let the 

temperature be raised by the ex- 
ternal application of heat. 

Common experience shows that 

A^; /'''^V V >j- this rise of temperature will be 
\l'i"/)\\\'i accompanied by a slight increase 
of volume, and refined experi- 
ment leads to the belief that it 
will also be accompanied by cer- 
tain intramolecular changes. Be- 
cause of the volume increase some 
of the heat supplied in raising 
the temperature must be used in 
doing the external work of lift- 
ing the weight W and the piston 
against the action of gravity, and 
of moving the piston against the atmospheric pressure on its 
upper side. This part of the total heat supply may be called 
AE. Because of the intramolecular work and because the mole- 
cules must be separated against any interattractions, as the vol- 
ume increases, some of the heat applied during the temperature 
increase must be used for doing internal work and may be desig- 
nated by A7. The part of the heat supplied and not accounted 
for by the sum of A£ and A/ must be that used in what is rec- 
ognized as a rise of temperature and may therefore be designated 
by A^, the sensible heat. 

Then the total heat (A(3) supplied during the temperature 
rise is AQ = A5 + A/ + AE. 

It so happens, however, that in this case, in which water is 
heated, the numerical values of A/ and A£ are so very small, as 
compared with that of A^, that for engineering purposes they 
may be neglected without serious error and A(2 may be taken as 
equal to A^, as illustrated at a in Fig. 2. 

(e) Suppose, now, that the temperature of the water in the 
cylinder has been raised to that at which steam is formed. Then 
continued addition of heat will not further raise the temperature, 
but it will cause the formation of steam (at constant tempera- 
ture and constant pressure) , with a very great increase of volume, 



ELEMENTARY LAWS OF HEAT ENERGY 13 

and its accompanying separation of molecules. There will also 
probably be certain intramolecular changes. 

As there is no temperature change during the process of 
vaporization, no part of the heat (A(2) supplied can be used to 
change the sensible heat, that is, as A5. 

The enormous increase of volume during vaporization, with 
the consequent raising of the piston against the resistance 
offered by the weight of the piston, the superincumbent at- 
mosphere, and the weight W, involves the doing of external 
work, and some of the heat supplied during the process must be 
used for that purpose. This heat, which may be designated by 
AE, is known as the external latent heat of vaporization and is 
stored as potential energy in the mechanical parts of the system, 
not in the steam itself. 

The intramolecular and the intermolecular work consume the 
rest of the heat supplied, and the part used for such purposes is 
called the internal latent heat of vaporization. According to 
the symbols adopted it would be designated by A/. 

Thus the heat supplied during vaporization is 

A(2 = A/ + AE, 

and this is shown at & in Fig. 2. 

Considering the whole process of heating the water and vaporiz- 
ing 

A(3 = ^Sl + Ml + ^El + A/„ + AE„ 

in which the subscript I indicates heat added to the liquid while 
raising the temperature and subscript v refers to the heat added 
during vaporization. On the assumption that A/; and AE; 
are negligible, 

AQ = ASi + A/„ + AE„. 

While water has been used as an example, all liquids present 
similar phenomena during heating and vaporization. Liquid 
ammonia, liquid sulphur dioxide, liquid carbon dioxide, or any 
one of a number of other materials, might have been used as an 
illustration. 

Other examples of processes showing the different utilizations 
of heat might be cited, but it is believed that, for present pur- 
poses, the one given above sufficiently illustrates the ideas and 
the meanings of the symbols used. 



14 HEAT-POWER ENGINEERING 

12. Specific Heat, (a) As just indicated, the change of tem- 
perature, with corresponding change of sensible heat, may be 
accompanied by two other changes, and it is clear that the change 
in associated heat energy is dependent upon all three factors. 
This must be taken into account in considering specific heat, 
which may be defined thus : 

The specific heat of a substance is the heat added to, or abstracted 
from, a unit weight of that substance when its temperature is changed 
one degree. 

The quantity of heat thus defined may be used in any one or 
all of three ways: (i) to raise temperature, (2) to do internal 
work, (3) to do external work. The quantity of heat required 
simply to raise the temperature would obviously be less than the. 
quantity required to raise the temperature and also to do work, 
external or internal. Hence for every substance there must 
be several specific heats, the values of which depend upon the 
use made of the heat. 

1 But by whatever method the heat is applied and whatever the 
use made of it during its addition to a substance, if the method is 
the same throughout, the specific heat, C, by definition must be 

C = ^ , (2) 

W{T2- Ti) 
in which 

A(2 = heat added. 

W = weight of substance receiving heat. 
Ti = temperature before A(2 is added. 
T2 = temperature after LQ is added. 

(b) If the specific heat is not constant, with any method of heat 
•application, the value of C from Eq. (2) is diVi average value for 
the temperature range and is called a Mean Specific Heat.* 

Hereafter mean specific heats will be denoted by putting a 
vinculum over the symbol, and, where essential, the temperature 
range will be indicated by subscripts; thus, C75-180 should be read 
as the mean specific heat between 75° and 180°. 

If the specific heat is constant the heat added during the tem- 
perature change from Ti to T2 is 

A(2 = CW{T,- T,) (3) 

* The mean specific heat is thus useless for purposes of exact calculation unless 
the temperature range over which it is the average is known and unless it is used 
in calculations involving that same temperature range. 



ELEMENTARY LAWS OF HEAT ENERGY 15 

If the specific heat is variable 

AQ= CW(T,-Tr) (4a) 

or = W n CdT, (4b) 

in which C represents the successive, or instantaneous, values 
of the variable specific heat as the temperature changes from 
Ti to T2. 

(c) It is conceivable that the temperature of a substance may 
be raised in such manner that no internal or external work is 
done, and the heat would then be applied only to raising tem- 
perature, and would be a true specific heat. Such true specific 
heats, it will be found later, are sometimes closely approximated 
in the case of gases. 

13. Total Associated Heat. It is impossible at present to 
determine the total quantity of heat energy associated with a 
substance under given conditions, because no means are available 
for complete heat removal. 

To compare associated heats of substances at different tempera- 
tures, a convenient value for Ti is assumed as a datum and 
calculations are confined to the region above it. This method 
gives relative and not absolute results, but serves for engineering 
purposes. The value of Ti is usually 32° F., when such a choice 
is possible. 



CHAPTER III. 

THE HEAT-POWER PLANT. 

14. General. It has already been stated that the heat-power 
engineer has to do largely with the conversion of the latent 
heat in fuels into available mechanical energy. This transfor- 
mation is effected by means of various pieces of apparatus, 
used singly in some cases and in series in others. All of the 
apparatus necessary in any individual case may be called a 
" Power Plant." 

That part of the power plant which receives heat energy and 
delivers mechanical energy, i.e. the "engine," is often called a 
"Prime Mover." ■, 

Examples of heat-power plants are familiar to all. They may 
contain Steam Engines and Boilers, with certain auxiliary 
apparatus necessary for the satisfactory operation of these two 
principal pieces; they may contain Gas Producers and Gas 
Engines, with suitable " auxiliaries;" or they may contain an 
engine only, as in the case of a gasoline-engine or an oil-engine 
power plant. 

No matter what the type of plant, a certain general method of 
operation is common to all. This is illustrated in Fig. i. Heat, 
from some kind of fuel, is continually flowing in, forming a 
" stream of energy." This energy leaves the system in a number 
of different ways, divisible broadly into waste (or lost) energy 
and useful energy. In all plants, including those theoretically 
perfect, there must always be a loss; thus the energy flowing out 
in useful form must always be only a fraction of that flowing in. 
This will be illustrated by the description of the operation of 
the Steam-Power Plant, in Section 15, and of the Producer Gas- 
Power Plant, in Section 16. 

15. The Steam-Power Plant, (a) This type, which is the 
oldest and is the most used of all forms of heat-power plant, 
may be said to consist of four essential parts, — the "Steam 

16 



THE HEAT-POWER PLANT 1 7 

Boiler," including the " furnace," the " Steam Engine," the 
" Condenser," and the " Boiler Feed-Water Pump." It is 
shown in one of its many forms in Fig. 3, with these four parts 
named. The method of operation is as follows. 

(b) Fuel is burned on the "grate " in the furnace under the 
boiler. The combustion of this fuel liberates a large amount of 
heat energy, which is partly absorbed by the products of com- 
bustion, partly radiated to the water through the " heating sur- 
faces " of the boiler tubes and shell, and partly radiated through 
the furnace walls to the surrounding air. This latter type of 
radiation represents a loss, which can never be prevented, as the 
furnace walls cannot be made nonconducting. 

The furnace may be regarded as the part of the boiler apparatus 
which converts the heat energy, latent in the fuel, into available 
heat energy. It will be found that there are certain losses in 
this conversion which can never be entirely prevented in any 
real case. They may be summarized as follows: 

(i) Some of the fuel falls through the grate and is not burned. 

(2) The ashes and refuse drop through the grate with a 
higher temperature than that at which they were put into the 
furnace. 

(3) Some of the more volatile parts of the fuel pass off with 
the products of combustion and are not burned. 

(4) In order to insure the complete combustion of the fuel, 
a larger amount of air must be supplied the furnace than is 
theoretically necessary. This mixes with the products of com- 
bustion proper and represents just so much more gas to be 
heated by the energy liberated by combustion. As a result the 
temperature attained by these gases is proportionately lower and, 
as will be discovered later, the subsequent utilization of the heat 
is made more difficult. 

(c) During the operation of the furnace a stream of radiant 
heat energy from the incandescent fire passes through the heat- 
ing surfaces to the water and steam, and there is also a stream of 
hot gas which, as it passes over these surfaces, gives up heat to 
the fluids within. In this part of the process there will always 
be three losses: 

(i) Part of the heat carried by the products of combustion 
will pass out through the external walls of the " boiler setting," 
instead of into the heating surfaces. 



i8 



HEAT-POWER ENGINEERING 




^^ 



THE HEAT-POWER PLANT 1 9 

(2) The gases can in theory pass heat into the heating surfaces 
so long as their temperature is higher than that of the water and 
steam. In the ideal boiler these gases would be cooled to the 
temperature of the water and steam, but in practice, for vari- 
ous reasons, they leave the apparatus when there is still a dif- 
ference of temperature of from 200° F. to 500° F. or even 
more. 

(3) The temperatures of the fuel and air entering the furnace 
of course approximate that of the room, and the products of 
combustion are heated from that value (about 60° F.) to the 
high temperature with which they leave the furnace. The 
temperature of the water and steam within the boiler is always 
from about 200° to 400° F., or more, higher than room tem- 
perature; thus, even if the gases were cooled the theoretically 
maximum amount, they would still carry off considerably more 
heat than they would if cooled to atmospheric temperature. 

Despite all the losses so far enumerated, a considerable pro- 
portion (from 50 to 80 per cent) of the original heat energy of 
the fuel is passed through the heating surface and is used in 
raising the temperature of the water and in generating steam. 
This heat is stored in the steam. 

(d) As was explained in Section 11 (d), under the conditions 
governing the generation of steam in a steam boiler, the liquid 
must first be raised to a definite temperature, dependent on the 
pressure, before it can be vaporized. To raise the water to this 
temperature a certain amount of heat must be added to it; and, 
the lower the temperature at which the water enters the boiler 
and the higher the temperature of the steam, the greater will 
be the quantity of heat needed. 

After the absorption of this amount of heat a still larger 
quantity, known as the " latent heat of vaporization," must be 
supplied to convert the hot water into steam at the same tem- 
perature. 

The total heat supplied can be subsequently abstracted, as 
heat, by condensing and cooling and thus obtaining the same 
water at the original temperature, or part of it can be obtained 
in the form of useful mechanical energy by certain transforma- 
tions which may be made to take place in the steam-engine 
cylinder. For our present purposes this latter is the more 
important of the two possibilities. 



20 HEAT-POWER ENGINEERING 

(e) The steam is led to the cyHnder of the steam engine by 
the " steam pipe " shown in Fig. 3. In the cyhnder a part 
of the heat in the steam is converted into mechanical energy by 
the action of the steam on the piston, part is wasted by " cylinder 
losses," which will be considered in a later chapter, and the 
remainder is still in the steam when this is discharged from the 
cylinder. Only from 5 to 22 per cent of the heat available in 
the steam is converted into useful energy in the cylinder, and, 
because of friction of engine parts and work done in driving the 
pumps, not all of this is delivered by the engine to the belt or 
other power consumer. 

The exhaust steam, still retaining the greater part of the heat 
that was furnished by the fuel, is conducted to the " surface 
condenser" (see Fig. 3), where it is condensed on the outer 
surfaces of the condenser tubes, through which the " condensing 
water " is circulated. The heat which the condensing water 
absorbs in liquefying the steam is the " latent heat of vapori- 
zation," and this is large in amount. In the plant shown this 
heat is not further utilized and hence represents a considerable 
loss. 

The water resulting from the condensation of the steam, known 
as the " condensed steam " or " condensate," is transferred 
from the condenser, in which the pressure is below that of the 
atmosphere, to the " hot well " by the " vacuum pump," which 
also removes any air which may accumulate in the condenser. 
The " feed-water pump " takes this water from the hot well, 
with whatever heat it contains, raises its pressure to that of the 
steam, and returns it to the boiler, where it is reconverted into 
steam and started again on the round just described. 

(f) Such a combination of processes, which periodically brings 
the material back to starting conditions, is known as a "cycle," 
or, more properly, as a " closed cycle." 

The characteristic of the cycle above outlined is the fact that 
the water (or, speaking more generally, the " working sub- 
stance ") is not lost or used up or permanently altered in any 
way. It serves simply as a carrier and transformer of heat 
energy, receiving it from the boiler furnace, giving up some of 
it as mechanical energy to the piston, rejecting the remainder 
to the condenser, and then returning to the boiler to start the 
cycle once more. 



THE HEAT-POWER PLANT 21 

This is, in theory at least, characteristic of all processes by 
means of which heat is converted into work. In practice it is 
sometimes found to be simpler or more desirable to throw away 
the working substance after it has been used in the engine and 
to continue to supply new quantities for the reception of heat 
at high temperature. In steam-power plants, for instance, the 
condensate is often abandoned, and the boilers are then supplied 
with corresponding quantities of water from some other sources, 
such as wells or streams. 

Theoretically, however, it is immaterial whether one pound of 
water is used time after time, or whether new is substituted for 
old, pound for pound, at some point in the process, provided only 
that the substitute have the same volume, pressure, temperature, 
and heat conditions as that which it replaces. 

In the lower part of Fig. 3 is a " heat- flow diagram." This 
shows the stream of heat energy flowing from the boiler to the 
engine. Its width shows the relative amount of heat remaining 
available for doing external work, and the offshoots show the 
losses that occur at different stages of the process. 

(g) Returning to the engine, the action of the steam within the 
cylinder will now be considered in a very elementary manner, in 
order to bring out certain conceptions which will b.e useful in 
the discussions of the following chapters. This action of the 
steam will be considered in detail later. 

The steam, upon its arrival at the engine (which, for sim- 
plicity, will be considered " single-acting "), is admitted by the 
" admission valve " to one end of the cylinder, where it acts on 
the piston, causing it to move and deliver mechanical energy. 
The valve may remain open during the entire stroke of the piston, 
or it may close before the stroke ends, which is the usual practice. 

If the different positions of the piston in its stroke are plotted 
as abscissas and the corresponding pressures acting on the 
piston face are erected as ordinates, there will be obtained a 
line like ab, in Fig. 4, which line is a graphical representation 
of pressures occurring within the cylinder during the admission 
of the steam. The work done on the piston in moving it from 
position I to 2 can be computed if the constant pressure acting 
on the piston and the distance traversed are known. 

If the admission valve be assumed to close (at 2) when the dis- 
tance moved is less than the stroke, the expansion of the steam 




22 HEAT-POWER ENGINEERING 

thus entrapped will continue to drive the piston until the end of 
the stroke is reached. It will be discovered in later chapters that 
this expansion is accompanied by a drop in the pressure and in 
the temperature of the steam. The way the pressure drops 
during the expansion is shown by the curve be in Fig. 4. Th& 
work done while the piston is moving 
from position 2 to 3 can be computed 
when the average pressure acting on 
the piston and the distance traveled are 
known. The average pressure is pro- 
^ portional to the mean ordinate of the 
curve be. The method of determining 
it will be given later. At present it i& 
Pig , sufficient to know that work is done 

during this expansion. 
When the piston arrives at the end of its stroke the " exhaust 
valve " opens communication between the interior of the cylinder, 
and the condenser, in which a comparatively low temperature 
and pressure are maintained, and some of the steam at once 
rushes from the cylinder to the condenser, where it is liquefied 
and discharged to the hot well in the manner already discussed. 
This process is shown by the line cd in Fig. 4, the pressure within 
the cylinder decreasing to the value prevailing within the con- 
denser. 

If, now, the piston is driven back to the beginning of the 
stroke, it will force all the steam from the cylinder into the 
condenser, where it will be liquefied as fast as it enters. In 
moving from position 3 to i, in Fig. 4, the piston will have swept 
through the entire stroke against a constant resisting pressure 
equal to the " back pressure " or " condenser pressure." This 
operation is represented by the line de in Fig. 4. In forcing 
the steam from the cylinder, the piston does work which can be 
computed if the mean resisting pressure, as shown by the ordi- 
nate of de, and the stroke are known. 

Obviously, no work is done on or by the piston during the 
process represented by ed, as it is not accompanied by motion of 
the piston. Similarly, if the piston is stationary at the beginning 
of its stroke while the pressure is raised by the entering steam 
from the value shown at e to that at a, no work is done during 
that process. 



THE HEAT-POWER PLANT 23 

The total work done during the two strokes is the difference 
between the work done on the piston during processes represented 
by lines ah and be and that done on the steam by the piston during 
process de. 

The processes through which the steam has been carried in the 
cylinder (as shown in diagram, Fig. 4) are idealized versions of 
what occurs in actual engines, and it is seen that even in this 
ideal case only a small part (theoretically, from 10 to 30 per cent) 
of the heat in the steam could be actually converted into work, 
the rest remaining in the steam exhausted. In the actual case a 
still larger amount of the heat is wasted in the cylinder and a 
proportionately less amount of heat is delivered as mechanical 
energy to the piston. These losses occurring within the cylinder 
are quite large and may be called " cylinder losses." 

Not all the mechanical energy that is available at the piston 
is delivered by the engine (by belt or other means) for doing 
useful work, for some of this energy is used in overcoming the 
friction of the engine itself. 

The relative amounts of energy available for doing work and 
the losses occurring at the different stages are shown in amount 
by the width of the energy stream in the lower part of Fig. 3. 

(h) In imagination at least, it may be considered that the 
same operations that have been described for the power plant as 
a whole can be performed entirely within the engine cylinder 
alone. Thus the water (or working substance), constant in 
amount, can be considered as always remaining within the cyl- 
inder, and can be imagined first as being there heated and vapor- 
ized (corresponding to lines ea and ab in Fig. 4), then as steam 
acting on the piston during the expansion (corresponding to 
line be in Fig. 4), and finally as being condensed and returned 
to its original condition (according to lines cd and de) by the 
abstraction of heat by some process equivalent to that per- 
formed by the condenser. 

As all these processes are imagined to be performed with the 
same working substance, and as this is always returned to its 
original condition, the operations within the cylinder may be said 
to constitute a cycle, which may be called "the engine cycle " 
to distinguish it from the cycle of the power plant as a whole, 
(i) It should be noted that, in obtaining mechanical energy 
from heat by means of the engine, the working substance supplies 



24 HEAT-POWER ENGINEERING 

heat energy to the engine at a high temperature (that is, it fur- 
nishes what may be called "high-temperature heat"), and that 
upon leaving the cylinder the working substance still retains 
some of the heat but at a lower temperature (that is, it retains 
what may be called " low- temperature heat "). This will be 
found to be characteristic of every process by which heat is con- 
verted into mechanical energy. Evidently, the more heat con- 
verted into mechanical energy and the less rejected at low 
temperature, the more efficient is the engine. But even in the 
ideal case it will be found that some heat must be rejected, 
which is in accordance with the statement of the Second Law of 
Thermodynamics and is shown diagrammatically in Fig. i. 

i6. The Producer Gas-Power Plant. The principal parts of 
this plant are represented in Fig. 5. The fuel enters the gas 
producer, carrying with it its store of heat. In the producer 
the combustible part of this fuel is gasified at the expense of 
some of its heat, while in theory the rest of its heat is stored in 
the combustible gas formed. The gas, carrying this part of the 
heat with it, enters the engine cylinder, mixes with air, and is 
ignited. The resulting inflammation raises the temperature and 
pressure of the products of combustion to high values. These 
gases then do work on the piston at the expense of this high- 
temperature heat and sustain a corresponding drop in tem- 
perature. They are finally rejected, carrying with them a certain 
part of the original heat content, now existing at a lower tem- 
perature. 

Theoretically, it would be possible to remove this low-tem- 
perature heat in an apparatus corresponding to a condenser, 
return the same mass of working substance to its original chemical 
composition, and start the cycle over again. Practically, how- 
ever, it is found much simpler to throw the burned gases away 
each time and to start again with fresh working substance. 

For this reason the atmosphere is commonly used in place of 
a condenser. It possesses the necessary characteristic of low 
temperature, as compared with the highest attained in the opera- 
tion of the engine, and has ability to absorb all the heat rejected 
by the engine. It possesses the further convenient characteristic 
of being able to absorb the working substance as fast as it is 
rejected by the engine. 



THE HEAT-POWER PLANT 



25 




26 HEAT-POWER ENGINEERING 

Although the series of operations that was outhned in con- 
nection with the steam-power plant is not quite so evident 
in this case, analysis will show that, in theory at least, the 
working substance could be used over and over again, serv- 
ing only to receive high-temperature heat, to transform some 
of it into mechanical energy, and to reject the rest at a low 
temperature. 

17. Analogy. The operation of heat engines has often been 
compared to the operation of water wheels, and there is much 
that is similar. 

A water wheel develops mechanical energy by receiving water 
under a high head, absorbing some of its energy, and then re- 
jecting the fluid under a low head. 

A heat engine, in developing mechanical energy, receives heat 
energy at a high temperature (head), absorbs some of it, which 
is converted into mechanical energy, and then rejects the rest 
at a low temperature (head). 

This analogy between " heat sliding down a temperature 
hill," as it is sometimes stated, and " water sliding down a 
grade," is very useful, but should not be carried too far. 

One point of resemblance is, however, worthy of special note: 
The water wheel never removes all of the energy of the water; 
there is always a certain discharge loss, or a certain amount of 
energy rejected. In the same way the heat engine never removes 
all of the heat energy from the working substance; there is 
always a certain discharge loss, or a certain amount of energy 
rejected (Second Law of Thermodynamics). 

18. Further Study. A number of theoretical considerations 
must be studied in detail before this subject of conversion of 
heat energy into mechanical form can be discussed more thor- 
oughly. It is necessary to learn some of the physical and 
chemical properties of the common working substances, some 
of the different kinds of changes they can be made to undergo 
for the doing of work, and to develop certain theoretical cycles 
of operation upon which the real cycles are based. 

This is done in the immediately succeeding chapters. Gases 
are considered first because their laws permit of simpler forms 
of expression and are more easily understood than are those of 



THE HEAT-POWER PLANT 27 

-vapors, which are the only other working substances commonly 
used. 

In later chapters the real cycles, the engines, and their auxil- 
iaries, the power plants, and the commercial and operating con- 
siderations connected therewith, will be taken up again. 



CHAPTER IV. 

THE LAWS OF GASES. 

19. States of Aggregation of Substances, (a) Almost every 
substance known has, under proper temperature and pressure 
conditions, been made to exist in three physical states, or condi- 
tions of aggregation, — namely, as a solid, as a liquid, and as a gas; 
and it is probable that this can be done for all matter with proper 
regulation of temperature and pressure. 

The higher the temperature and the lower the pressure, the 
greater the tendency to exist in the more rarefied condition of 
aggregation — that is, as a gas; while the lower the temperature 
and the higher the pressure, the greater the tendency toward the 
solid form. The values of the limiting conditions, — namely, tem- 
perature and pressure, — which will determine any of the three 
states, vary widely with the different substances, and under 
ordinary atmospheric conditions some of the materials in the 
universe are known as solids, others as liquids, and still others 
as gases. 

The various substances obey certain laws, differing for different 
states, and with constants that vary with the substance. The 
laws that govern matter in the gaseous state are the simplest 
and at present are best known. These laws will now be de- 
veloped and will be more fully discussed in Chapter IX. 

(b) The laws of gases may be divided into two groups, — 
Ideal Laws and Actual Laws. 

The ideal laws or laws of ideal gases are not absolutely true 
for any real gases, but hold, with sufficiently close approximation 
for engineering purposes, for all gases which are far removed 
from liquefaction, like hydrogen, nitrogen, oxygen, and, to a 
certain extent, carbon dioxide. 

The actual laws of gases are the ideal laws modified so as to 
conform as accurately as possible to the behavior of real gases, 
and they generally take account of different theories of the 

28 



THE LAWS OF GASES 29' 

actual composition of gases. They are seldom used by engineers 
and their consideration is left for another chapter. 

In general, the variation from the ideal laws becomes less as 
the real gases are further removed from the conditions of lique- 
faction, or as the molecules become more widely separated and 
the effect of intermolecular forces becomes less. From this it 
is concluded that the hypothetical ideal gas must be imagined 
devoid of such intermolecular forces. 

20. The Ideal Laws of Condition of Gases. These laws are, 

1. The Law of Boyle or of Marriotte, and 

2. The Law of Charles or of Gay Lussac. 

I. Boyle's Law. 

This law, which deals with variations of pressure and volume 
at constant temperature, is: 

When the temperature of a given weight of gas is maintained 
constant the volume and pressure vary inversely. Mathematically 
expressed, it becomes 

Yi-^ (5) 

or 

FiPi = F2P2 = F3P3 . . = VnPn = Constant, . (6) 
in which 

Vi, V2, etc. = the volumes occupied by a given weight of a 
particular gas at constant temperature but 
different pressures, and 

Pi, P2, etc. = the corresponding pressures exerted by the 
gas, or to which the gas is subjected. 

2. Charles' Law. 

(a) This law, which deals with volume or with pressure 
changes accompanying temperature variations may be con- 
veniently divided into two statements : 

(i) When the pressure of a given weight of gas is maintained 
constant the volume increases -^^2* of its value at 32° F. for every 
Fahrenheit degree rise of temperature and decreases the same amount 
for every degree decrease of temperature. 

* The exact value is not -f\^, but this is probably the nearest simple fraction 
and is close enough for engineering purposes. 



30 HEAT-POWER ENGINEERING 

(2) When the volume of a given weight of gas is maintained 
constant the pressure increases 4^2 of its value at 32° F. for every 
Fahrenheit degree increase in temperature and decreases the .same 
amount for every degree decrease in temperature. 

(b) Given a unit volume of gas at 32° F. with pressure main- 
tained constant, then increasing the temperature 1° F. would 
cause the volume to become 4^2 larger, while a decrease of 1° F. 
would result in a volume 4^2 smaller; a 2° change in temperature 
would cause the volume to alter 4I2, and so on. Writing tem- 
peratures and corresponding volumes for this case side by side, 
and beginning with a temperature of (492 + 32) degrees, gives: 

Temperatures, Fahr. Volumes 

524° (= 32 + 492) . . I + (492 X 4^2) = III = 2 

33° I + ( I X 4^^) = III 

32° I + ( o X 4^2) = III = I 

31 I — (iX 4^2) = Hi 

0° ....... I - ( 32 X 4^2) = m 



- 460° ( = 32 - 492) . . I - (492 X 4*2) = 4I2 = o. 

If these volumes are plotted as abscissas with tempera- 
tures in degrees Fahr. as ordinates, the points will be found 
to lie on a straight line which intersects the temperature axis 
at - 460°. 

If the law holds consistently the volume will be reduced to 
zero at — 460° F. Similarly with constant volume the pressure 
must become zero at — 460° F. This point of the temperature 
scale is called the Absolute Zero of temperature, and tempera- 
tures measured from it are known as Absolute Temperatures. 
Since this point is 460 Fahrenheit degrees below Fahrenheit zero, 
the absolute temperature, T, corresponding to any Fahrenheit 
temperature, t, can be found by adding 460 to the latter; that is, 

r = 460 + / (7) 



THE LAWS OF GASES 31 

(c) The conception of absolute temperature makes possible a 
very simple mathematical statement of Charles' law. This 
should be evident from the foregoing table. 

Thus, the two parts of the law are: 

(i) With pressure constant ^=^. (8) 

V2 J- 2 
and 

(2) With volume constant ^ = ^ (9) 

-r2 ^2 

(d) The apparent anomaly of zero volume at absolute zero 
temperature results from assuming the law to hold continuously 
to the lowest temperatures. It should be remembered that this 
is a law for an ideal substance only, and does not represent the 
behavior of any material actually existing. Therefore there is no 
a priori reason for doubting the result. A possible explanation 
of this matter will be given in Section 76 (e). Despite its appar- 
ently ridiculous meaning at low temperatures, the law holds with 
sufficient accuracy for most gases at the temperatures used in 
ordinary engineering, 

3. Combination of the Laws of Boyle and Charles. 

(a) Since it is seldom true in actual practice that one of the 
three possible variables, P, V, and T, remains constant while the 
other two change, it is convenient to combine Boyle's law with 
that of Charles so as to obtain an expression giving the relation 
among all three variables. The resulting expression is known as 
the Law of Condition of Ideal Gases, or, more simply, as the Law 
of Ideal Gases. 

(b) To obtain the mathematical expression of this law, it is 
only necessary to imagine a given weight of gas with initial con- 
ditions Pi, Vi, Ti, changing to final conditions P^, V2, T2, in two 
steps; first, at constant temperature Ti, to V2 and some inter- 
mediate pressure Pi, and second, at constant volume V2, to P2 
and T2. 

The result of the first change is given by Boyle's law as follows : 

y p ' 
With temp, constant at Ti, -z^ = -75-, 

V2 Pi 

from which P/ = ^ll^. ...... (10) 

V2 



32 HEAT-POWER ENGINEERING 

Here Pi is the resulting pressure of the gas when its volume is 
changed to F2 and its temperature remains Ti. Then using 
Charles' law for the second change, 

with volume constant at F2, -^ = ^, 

P2 1 2 

from which p,=ilJl. (II) 

Here P2 is the resulting pressure of the gas when its temperature 
changes to T^ and its volume remains V^. 

If now the value of Pi from (10) be substituted in (11), the 
resultant expression is 

p _ P.Vi T, 

giving, on rearrangement, 

PyVi ^ P2V2 /j2) 

Ti Ta ' 

which is the expression sought. In general this becomes 

PlVl P2V2 P3F3 PnVn 



Ti T2 Ts 



= Constant. , . (13) 



(c) The value of this constant for any given gas will vary 
directly with the weight of gas dealt with ; for, at any given tem- 
perature and pressure, two pounds of gas must occupy twice the 
volume occupied by one pound, three pounds three times the 
volume, etc. For convenience it is customary to tabulate, for 
all the commercial gases, the value of this constant obtained by 
substituting in (13) the volume of one pound of gas and the tem- 
perature and pressure at which the volume was experimentally de- 
termined. This constant, commonly represented by R, will be 
found to be of great importance. 

To distinguish the volume of any given weight from the 
volume of a unit weight of gas, the former will hereafter be desig- 
nated by V and the latter by V. The expression of the law for - 
one pound of ideal gas then is 

PV 

^=R (14) 

(d) It makes no difference what units are adopted in such an 
expression as (13), provided the same units are consistently used 
throughout all the calculations, but in (14) a constant R is dealt 



THE LAWS OF GASES 33 

with whose values have been calculated and tabulated, hence it 
is necessary to employ the same units as those used in calculating 
R. In English-speaking countries, 

P — pressure in pounds per square foot ; 

V = volume of one pound of gas, in cubic feet ; and 

T = absolute temperature in Fahrenheit degrees. 

(e) The ' ' constant ' ' in equation ( 1 3) may now be interpreted as 
WR where W represents the number of pounds of gas represented 
by Fi, F2, . . . Vn- This applies in all cases in which P stands 
for pressure in pounds per square foot, V for volume in cubic feet, 
and T for degrees Fahrenheit above absolute zero. 

(f) Boyle's law as previously stated may now be seen to be only 
a special form of equation (13) or (14). Writing these 

PV = WRT and PV = RT, 

it becomes evident that the right-hand member is a more complete 
expression for the " constant " of equation (6). 

21. The Specific Heats of Ideal Gases. As a result of the 
assumption regarding the constitution of ideal gases (see page 29) , 
it follows that, if a quantity of heat, A(2, is added to an ideal 
gas in such manner that it does not alter the gas chemically nor 
change its motion as a whole, equation (i) must become 

^Q = ^s+^E (15) 

because, as there are no positive or negative internal forces to 
overcome in such a gas, no heat is needed for doing internal work; 
hence A/ equals zero. Therefore the specific heat of an ideal gas, 
or the heat required when the temperature of an ideal gas is 
raised one degree, can only supply that needed to increase the 
temperature and to do the external work corresponding to any 
resultant volume change with the displacement of surrounding 
media. 

22. Constant- Volume Specific Heat of Ideal Gas (C^). (a) If 

the volume of an ideal gas is maintained constant while the 
temperature is raised, the pressure will increase according to 
Charles' law. As the volume does not change, no external work 
can be done because no external media are displaced. All the 
heat supplied must then be used for changing the temperature; 



34 HEAT-POWER ENGINEERING 

that is, using A(3« to designate the heat supplied with volume 
maintained constant, 

A(2^, must equal A^,,. 

li Cv represents the specific heat of an ideal gas when heated 
at constant volume, this equation may be written 

^Q,^ j\S.=WC,{T2-Ti), .... (i6) 
from which 

C = ^ (17) 

W as before standing for the weight of the gas and (T2 — Ti) 
being the temperature change. As already explained, the value 
of Cv thus obtained might be either a real constant or it might 
be an average over the range from Ti to T2. 

(b) Obviously this specific heat is a True Specific Heat as 
defined on page 15. Also, it is not only the heat required to 
raise the temperature of one pound one degree at constant 
volume, but is likewise the amount given out when the tem- 
perature drops one degree under the same conditions. 

(c) The symbol Cv denotes a certain quantity of heat energy 
measured in British thermal units, but as it is sometimes neces- 
sary to refer to the same quantity of energy in the mechanical 
form it is convenient to have a symbol for that purpose. For 
this Kv is used. As Cv stands for a certain number of thermal 
units, each of which is equal to 778 foot-pounds (see page 6), 
it follows that Kv must numerically be 778 times as large as C«; 
that is, 

778Cv- Kv (18) 

expresses the relation between the constant-volume specific heat 
in heat units and in units of mechanical energy. 

(d) It is now pertinent to inquire whether Cv is a constant for 
all conditions of the same gas. That is, whether it takes the 
same amount of heat to raise the temperature of unit weight 
one degree at constant volume when the gas is at a high tem- 
perature and when it is at a low temperature; whether it takes 
the same amount of heat with the gas at a low pressure but 
occupying a large volume as it does with the gas at a high pressure 
but occupying a small volume. 

Experiment and reasoning lead to the belief that Cv may be 
considered constant for all temperatures and pressures in the 



THE LAWS OF GASES 35 

case of the Ideal gas, that is, one having only the properties 
assigned to that material in previous paragraphs. 

In the case of real gases, experiments prove Cv to change 
with variation of temperature and pressure; but for ordinary 
gases through usual temperature ranges the variations are 
negligible. With exceptionally high temperatures, such as. 
those occurring in furnaces and the cylinders of internal-com- 
bustion engines, the increase in the values of Cv is very noticeable. 
Therefore it is customary to treat Cv as a constant for real 
gases except when making accurate calculations for very high 
temperature conditions. 

(e) Since, as shown on page li, the intrinsic heat energy of a 
substance depends only upon the content of sensible heat and 
the heat expended on internal work, it follows from the fore- 
going that in the case of ideal gases the intrinsic heat energy depends 
only on the temperature. It is impossible to measure the total 
intrinsic heat energy of a gas because it cannot be completely 
removed. It is, however, possible to measure the quantities 
concerned in changes of intrinsic energy, and this is what is 
commonly done. Whatever the conditions of the change, if the 
temperature of W pounds of gas is altered from Ti to T^, the 
Change of Intrinsic Heat Energy is 

A(3„- WCv {T,- TO (19) 

23. Constant-Pressure Specific Heat (Cp). (a) If the pres- 
sure of an ideal gas is maintained constant while the temperature 
is raised, the volume will increase according to Charles' law. 
As the volume changes, surrounding media must be moved under 
the constant pressure they exert upon the gas, and hence heat is 
expended not only in adding intrinsic energy, but also in doing 
external work AEp. The amount of heat required is, then, 

AQp= A5p+ AEp= WCp {T2 - Ti), . . . (20) 
from which the specific heat at constant pressure Cp is, 

c = ^ r2i) 

Here, as in the preceding case, the specific heat may also be 
given in units of mechanical energy, in which case the symbol 
Kp is used. Evidently 

77SCp-^Kp (22) 



36 HEAT-POWER ENGINEERING 

(b) It was shown in Eq. (19) that the change of intrinsic 
energy depends only on temperature change and is independent 
of pressure and volume conditions. Hence, whether an ideal 
gas is heated one degree at constant pressure or at constant 
volume, the change of sensible heat is exactly the same, and it 
follows that the constant-pressure specific heat exceeds the constant- 
volume specific heat by just the quantity of energy necessary to 
do external work, AEp. That is, for any temperature variation, 
Ti to T2, 

ASp = AS^, 

-giving AQp = AQ, + AEp, 

AE 

^"d ^^^^- + PF(r2-ro ^^^^ 

(c) A simple expression may be obtained for the external 
work' done when a gas is heated at constant pressure. Imagine, 
for instance, that one pound of gas with conditions Vi, Pi, Ti, is 
confined in a cylinder with a movable piston of area F square 
feet. The length of the portion of the cylinder lying between 
the inside of the head and the face of piston must be 

Vi 
Li= — feet. 

If now the gas is heated at constant pressure to T^. the volume 
will increase to F2 and the piston must move out so that the 
distance from the inside of the cylinder head to the face of the 
piston, becomes 

Li = -^ feet. 

But the piston will have moved through the distance L^ — Lx 
against a force Pi pounds per square foot; then the work done is 

External work = FPi (L2 — Li) 
= Pi {FU - FU) 
= Pi(F2- Fi)ft.-lbs.; . . . (24) 

hence the external work done when a gas is heated at constant pres- 
sure is the product of that constant pressure and the change of 
volume, the result being in foot-pounds. If measured in thermal 
units it would be 

External work = AEp = ^^^'7 ^'^ B.t.u., . . (25) 

77» 



THE LAWS OF GASES 37 

and if this be substituted in Eq. (23), understanding Vi and V2 
to stand for the volumes before and after a one-degree change, 
and remembering that the equation must be written in terms of 
the volume of one pound of gas, there results 

Using the foot-pound symbols 

K,= K. + P{N,-V,) (27) 

(d) The constant-pressure specific heat may now be shown to 
be a constant for an ideal gas. It has been seen that the con- 
stant-volume specific heat may be considered constant; then, if 
P (V2 — Vi) can be shown to be independent of temperature and 
pressure conditions, Kp and Cp must be constant. This amounts 
to proving that A£p per degree is constant at all temperatures, 
pressures, and volumes. 

To do this, imagine one pound of a gas with conditions Vi, 
Pi, Ti, first heated one degree to Ti with volume changing to Vi' 
and pressure remaining constant. The external work done will 
be 

External work = Pi (V/-Vi) . . . . (28) 

Then, if the condition of the same gas is changed to V2, P2, P2, 
which may be any values different from Vi, Pi, Pi, and if its 
temperature is then raised one degree to P2' with the volume 
changing to V2' and the pressure remaining constant, the ex- 
ternal work, as before, will be 

External work =P2(V2'- V2) (29) 

But by the law of ideal gases 

PiVi ^ PiVi^' ^ P2V2 _ P2V2' ^ 
Pi P/ P2 P2' 

Substituting from this in Eqs. (28) and (29) gives 

Work in first case = P (P/ - Pi) = R, 
Work in second case = R(T2 — P2) = R, 

so that the work is the same in each case. It follows that when 
the temperature of one pound of a perfect gas is raised one degree 
at constant pressure, the work done is always the same and is inde- 
pendent of the values of P, V, and T; that is, AEp per degree is 
constant. 



38 EEAT-POWER ENGINEERING 

More than this, it appears that R, previously known only as 
the constant in the law of ideal gases, is really equal to the foot- 
pounds of external work done when the temperature of one pound 
of gas is raised one degree at constant pressure. From this 

K^ = K. + R, (30) 

and C,= C. + -~. ...... (31) 

24. The Ratio 7. The ratio between the two specific heats 
of gases just considered is of great importance and is designated 
by the letter 7, thus, 

§! = & = -.. (3^) 

from which it is evident that 7 must always be a quantity greater 
than unity. 

By means of the ratio 7 a form of expression, which will be 
very convenient later, can now be developed from Eq. (30). 
Rearranging the latter and dividing by Kv, there results 

Kp R R 

Kv Kv Kv 

T3 

from which Kv = -, (33) 

7 — 1 

which is the expression sought. 

25. Table of Gas Constants, (a) The Gas Constants most 
commonly used by the engineer are given in Table I. In it all 
columns with headings having the same subscript are based upon 
data of the same character. Columns headed with the same 
letter, as Bi, B2, B3, contain values of the same quantity, for 
each gas, determined in different ways. In the first column of 
each of the groups B, C, and D is a closely approximate value 
calculated from data given in column Ai rounded oft to the 
nearest half -unit. Column A2 gives molecular weights based on 
the 1909 International Atomic Weights, and all other columns 
headed with the subscript 2 contain values computed from these 
weights. Columns headed with subscript 3 give experimentally 
determined values. 

(b) The calculated columns for Density depend on the Law of 
Avogadro. This law states that equal volumes of all gases, at 
the same temperature and pressure, contain an equal number of 



THE LAWS OF GASES 39 

molecules. Hence the densities of different gases must he in the 
same proportions as the molecular weights. The Weight per 
Cubic Foot, and Cubic Feet per Pound, columns C and D, can 
be obtained from the density columns. 

(c) While the specific heat Cp would be constant for an ideal 
gas, it is not constant for real gases. Experiment shows it to 
vary with temperature and pressure. The values tabulated in 
column E3 are average values for ordinary temperature ranges at 
atmospheric pressure. 

The values of 7, however, which are usually determined from 
the velocity of sound in the gas, are generally for some definite 
temperature. Therefore the numbers tabulated in column G3 
are not really on the same temperature basis as those given in 

column E3; hence, since the most satisfactory way of obtaining 

C 
values of C^ is by using the equation C„ = -^ , the values given 

7 
in column F3 must be in error with respect to the rest of the 

data. 

This is well shown by the variation of values for R in column 
I3' from those in columns I2 and I3. The values in I3' are ob- 
tained from the equation Kp — Kv = R, which should give very 
accurate results and the numerical values show wide variations 
from those determined in other ways. 

In general, it may be said that the amount by which the experi- 
mental results vary from the exact calculated values is a measure 
of the degree of imperfection of the gas under consideration. 

(d) For average engineering work it will suffice to use the ap- 
proximate or observed columns, dropping all but three significant 
figures ; further figures are given in the table to correspond to the 
supposed standard of accuracy of experimental determinations. 

(e) The method of calculating the values in the several 
columns is as follows: 



51 


= ^x^ 


D, 


= i/C, 




29 


D, 


= i/C, 


B, 


-xi;5 


Dz 


= l/Cz 


Bz 


= Observed 


Ez 


= Observed 


Ci 


= .080725 X -Bi 


Fz 


= £3/^3 


a 


= .080725 X B^ 


■ Gz 


= Observed 


Cz 


= .080725 X Bz 


H 


= Theoretical 



40 



HEAT-POWER ENGINEERING 






■Sfe I 






H O 


o i-i ;^vo 00 o" " 

W M M ^ <v,00 On 


^ O lo r^ 

no ro w 
Ol ON cs CO 

H O H H 


of 


II 


O o 


o o o o o o o 


O O o 


o o 


o o 



O r^ r^o O w <N vo O f^o 

00 t^ M lo rOOO On (N IJO cn 00 

t-~ On O O 00 r^OO IN On !N t^ 

OhmoOOO hOhh 



O O O O O O O 



O o o o o 



<N r- ^ O H 

r~. ^ ^ -* 00 

O O Oh w 

d o" o" o" o" 



ro cc o NO M n r^ 

OnnO no lO lO on O 

t-^ r^ i-t ir^ CO r--- ctn 
I^ On O ( 



^NO ^ 
ON c-1 ^ (N ( 



M ro ro 



o o o o o o o 



o o o o o 



O O Oh 

d d d d 





.r, 






















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„ 










































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t^ 








































lO 






IN 


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H O 


o 


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H O 


»- 


o 


H 


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O, 


o 





o 


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r^ On On OnnO IT^ lO On 

NO ^ VOO CONO O H 



O IN H O H O 






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H H H M O 



a c6 



OO NO 

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On ^ O 



O 00 <M t^ H 

O O O O O 

-+ ■* ^ Tt-00 



•a II 

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'no t^ NO O 



^S 

bS 



n tN-j n to CO 



■rl- lO lO 



as 






QSOP 



g-gooyM§ gogn^, '-'o 

53 ^ >^ l>>-H ^ 'ff nJ >.-H 3 ^ g g 



THE LAWS OF GASES 



41 



30 00 10 Tt 0^ t^ 


00 ^O t>.00 ■+ 


s 





ro ■* IN 00 T)-00 


to H r^ Tj-vo 
ro Tt- CO M r^ 


ON 






00 00 00 00 00 



in 








^ 


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^ 


































c^ 












tv- 
























r^ 


^ 






t^ 























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" 




" 


" 


l-l 




l-l 


" 






-* 




















(N 






























O O O ro o o o 



CO w O ■* ro 
O 10 <M -^ CO 

O ^ M LO -* 



00000 






„ 




„ ^ 










„ 




„ 











„ 
































NO 




r^NO 


8 














t^ 




^ 








00 




On 00 






^ 




-* 


^ 




(N 


M 





01 


rf OnOO 


l_l 


<N 


H 


00 


CO 


10 


ro 





Ol 


J^ 


On 


^ 




;_^ 


" 


'-' 


" 














CS 





-7^ 5-^ 



00 O 00 On OnOO 



H 00 O CO 10 On 






OOw CONO-!i-lor^rO!N nOnOnOmnO 

OnOO 00 O 00 no OnOO <N m vo m nO On 

oOOn (MioOnOnminm cOOoOiOOi 



• c c C y 2* 



o§ 





ai 


















T! 
















^.%. 










(L 
T 




X! dt: « 












c 

Q 




(2 




0; 


o: 


(U 





0) 



o 3 3 iH V' o 



ooffiffi2;zo 









42 HEAT-POWER ENGINEERING 

I2* (Calculated from Inter, Atom. Wts. using Air as a Base.) 
^ 12.387 X 14-696 X 144 w I ^ ^ 

491.4 = (273 X 9/5) ^2 

I3 (Calculated from Specific Heats.) 

= 778 Cp - 778 C, = R. 
I3* (Calculated from Observed Volumes.) 

^ Ds X 14.696 X 144 ^ ^ 
491.4 = (273 X 9/5) 

* Although the value 492° is used in other parts of this book as the absolute 
temperature corresponding to 32° F., the value used in computing the quantities 
given in columns I2 and I3 is 491.4, because this corresponds to 273° C, which is 
used in most experimental determinations. 



CHAPTER V. 



EXPANSIONS AND COMPRESSIONS OF GASES. 

26. Volume Changes, (a) The law of ideal gases expressed 
by Eq. (13) shows that there are three inter -related variables which 
define the condition of a gas; namely, pressure, volume, and tem- 
perature. The fixing of any two of these determines the third. 
For the study of heat engines it is convenient to consider the 
behavior of the gas while the volume changes in various ways 
and to note the accompany- 
ing variations of the other 
two quantities. 

(b) Certain diagrams are 
useful in studying such 
changes, the most common 
one being called the pres- 
sure-volume diagram or PV- 
diagram. To construct this 
diagram pressures are plot- 
ted vertically and volumes 
horizontally as in Fig. 6. 

Assume, for instance, that 

the volume and pressure of a 

. 1 ^ r ^ . Fig- 6. — PV-Diagram. 

given weight of a certain gas 

are. Pi, Vi, as plotted at A. The volume of this gas may be in- 
creased or decreased in different ways. For example, volume 
might be made to increase or to decrease while pressure is main- 
tained constant. If the various volumes assumed are plotted at 
constant pressure Pi, the resulting points must lie on the line 
AB or on the line AC. Either one line or the other would then 
show graphically the relations of pressure and volume. The 
temperature at any point as P2 F2, where P2 = Pi in this case, 
could be found by substitution in Eq. (13) or (14), remembering 
that if the form involving R is used V stands for the volume of 
one pound of gas. 

43 




44 HEAT-POWER ENGINEERING 

(c) Volume-changes with volume increasing are known as ex- 
pansions; volume-changes with volume decreasing are known 
as compressions. Inspection of Fig. 6 shows that any number 
of different kinds of expansions are possible; any line drawn 
from A in the field to the right of DE represents a possible ex- 
pansion. Similarly, any line drawn from A in the field to the 
left of DE represents a possible compression. Really, all the 
expansions commonly used lie in the quadrant between AB 
and AE and all the usual compressions between AD and 
AC. 

(d) Since there are thus an infinite number of possible methods 
of changing volume, it is impossible to analyze all of them. 
Fortunately, the study of four characteristic methods of change 
— including the limiting case with volume constant — suffices 
for the elementary consideration of heat engines. They are: 

1. Volume changes, in which the pressure is constant; or, 
otherwise stated, in which the volume changes most rapidly 
with respect to pressure. These are known as Isobaric Changes 
and are represented by the graph AB or AC, Fig. 6. 

2. Pressure changes, in which the volume is constant; or, 
otherwise stated, in which the pressure changes most rapidly 
with respect to volume. These are known as Isovolumic Changes 
and are represented by the graph AD or AE. 

3. Volume changes at constant temperature, known as Iso- 
thermal Changes. 

4. Volume changes known as Adiabatic Changes (to be de- 
fined later). 

27. Constant-Pressure or Isobaric Changes of Gases. As 

just explained, the graph of such changes is a horizontal line on 
the PV-diagram. In Fig. 7 an isobaric expansion of gas with 
initial conditions PiVi would be represented by the line AB and 
a similar compression by the line AC. 

Equation for Isobaric Changes. 

(a) It is evident from an inspection of the graph of such a 
change, or from the definition, that its equation in P F coordinates 
is 

P = Constant (34) 



EXPANSIONS AND COMPRESSIONS OF GASES 



45 



Change of Associated Heat during Isobaric Changes of Gases. 

(b) During these volume changes at constant pressure the 
temperature must vary according to Charles' law; that is, the 
absolute temperature must 
vary directly as the volume. 
But when a unit weight of 
gas has its temperature 
raised or lowered one degree 
at constant pressure, it ab- 
sorbs, or gives out, a quan- 
tity of heat equal to its con- 
stant-pressure specific heat, 
Cp. Then for any weight W 
of gas changing volume from 
Vi to V2 at constant pressure 
with a corresponding change 
of temperature from Ti to 
T2, the change of associated 
heat (in thermal units) is 




Volumes 
Fig. 7. — Constant-Pressure Changes 



AQ= WCAT2- Ti). 



.... (35) 

If the volume change is an expansion the result will be positive 
because T2 will be greater than Ti; but if the volume change is 
a compression T2 will be less than Ti and the result will be 
negative. Negative heat change must be interpreted as heat 
given out or liberated, so that the equation as stated is true for 
compressions as well as expansions. 

Work during Isobaric Changes. 

(c) It was shown in Eq. (24) that the external work in foot- 
pounds done by a gas when its temperature increases with pres- 
sure constant is given by the equation 

External Work = 778 AE = P ( F2 - Fi) ft. -lbs. . . (36) 

This is the equation for work done during a constant-pressure 
volume change. The equation gives a positive result for expan- 
sion, and a negative one for compression; that is, a gas expand- 
ing at constant pressure does work, and work must be done ta 
compress a gas at constant pressure. 



46 



HEAT-POWER ENGINEERING 



(d) Obviously, the product P - {V2- Vi) is represented in 
Fig- 7> by the crosshatched area under the Hne showing the 
volume change from Vi to F2, hence the area under that line, 
expressed in foot-pounds, is equal to the work done during the 
volume change. For an expansion the area is interpreted as 
positive, that is, as the area ABGF; for a compression from 
Pi V2 to Pi Fi, as negative, that is, the area BAFG. This prop- 
erty of representing work by 
area is common to all PV- 
diagrams and makes them 
very useful. 

28. Constant-Volume or 
Isovolumic Changes of Gases. 

(a) With volume constant 
the pressure will increase as 
the absolute temperature in- 
creases, and decrease as that 
temperature decreases. The 
graph of such changes plotted 
to P F coordinates is a verti- 
cal line like ED in Fig. 8. 
There being no volume change, there can be no expansion or 
compression. A line drawn vertically upward, as AD, means 
pressure increase, and a line drawn vertically downward means 
pressure decrease. 

Equation for Isovolumic Changes. 

(b) The equation of constant-volume changes in terms of P 
and F must be 

F = Constant (37) 









D 
























A 
PiVi 
























E 







Volumes 
Fig. 8. — Constant-Volume Changes 



Changes of Associated Heat during Isovolumics of Gases. 

(c) To increase the temperature of one pound of gas one 
degree at constant volume requires a heat addition equal to 
C^ thermal units, and to decrease the temperature one degree an 
amount of heat equal to C^ must be withdrawn. Then if the 
pressure of W pounds of gas changes from Pi to P^ at constant 
volume, while the temperature varies according to Charles' law 



EXPANSIONS AND COMPRESSIONS OF GASES 



47 



from Ti to T2, the change of associated heat] (in thermal units) 
is 

AQ=WCAT2-T^) (38) 

For a pressure increase Charles' law shows that T2 must be 
greater than Ti and the result will be positive. For a pressure 
decrease, T2 will be less than Ti and the result will be negative; 
that is, heat must be supplied to cause increase of pressure at 
constant volume, and must be abstracted to cause decrease of 
pressure at constant volume. 

Work during Isovolumic Changes. 

(d) Since there is no change in volume, — that is, no displac- 
ing of surrounding media, — there can be no external work 
done. Then for this case, in foot-pounds, 

External Work = 778 AE = 0. . . . (39) 

In the figure given there is no area under the line represent- 
ing the change, and therefore, since area on the pressure-volume 
diagram represents work, it follows that the work equals zero. 



29. Constant-Temperature or Isothermal Changes of Gases. 

(,a) If the temperature of a gas is maintained constant, while its 
pressure and volume change, 
Boyle's law applies and gives 
the relation between these 
two variables as 

PV = Constant. 

If, starting with Pi Vi in 
Fig. 9, different values be 
substituted for V in this 
equation and the resulting „ 
pressures are computed and g 
plotted against these vol- 2 
umes, the graph obtained 
will be CB, which is a rec- 




Volumes 



Fig. 9. 



Isothermal Changes for Ideal 
Gases 



tangular hyperbola. The line 
from A to B shows an iso- 
thermal expansion from Pi Vi and the line from A to C repre^ 
sents an isothermal compression from the same point. 



48 HEAT-POWER ENGINEERING 

Equation for Isothermal Changes of Gases. 

(b) The equation of these changes, in terms of pressure and 
volume, must be that just given, 

PF= Constant (40) 

Work during Isothermal Changes of Gases. 

(c) Since there is a change of volume during isothermal 
changes, external work must be done. If in Fig. 9 the two closely 
spaced vertical lines represent a volume change 8 V, from Vi to 
V2, so small that the pressure may be assumed constant while it 
is taking place, the external work in foot-pounds during that small 
change must be 

778 8E = P (V2' - FiO = P [(F/ + 8V)-V,'] = P8V 

and for a finite change of any size, from Fi to F2 



778 AE 



,/''^- (41) 



To integrate this expression, it is necessary to substitute for 
P in terms of F. Assuming P and V as the values for any point 
on the curve and Pi and Vi as the values with which the expan- 
sion starts, 

PiFi = PV 
from which 

p^PiFx 
F 

Substituting this value in the expression (41) gives 

= PlFi(l0geF2-l0g.Fl) 

= PlFl loge*^^ ft.-lbs. ..... (42) 

If the ratio of volumes (F2/ Fi) in the last expression, known as 
the ratio of expansion or of compression, is designated by the 

* It is usually more convenient to use logio instead of loge. Since loge = 
2.302 logio, Eq. (42) may be written = PiFi X 2.302 logio t^ * The other logarithm 

Kl 

mic equations which are to follow may be similarly transformed. 



EXPANSIONS AND COMPRESSIONS OF GASES 49 

letter r, the equation for work done by any weight of gas may be 
written 

778 AE = Pi Vi \oge r ft.-lbs. . . (43a) 

For unit weight 778 AE = RTi loge r ft.-lbs. . . . (43b) 

If the expansion is negative, that is, if there is compression, 
the work done by the gas must be negative ; thus work must be 
done upon it to decrease its volume. 

It should be noted that / P dV is the general expression for 

fJ Vi 

the area under a curve drawn to P F coordinates and hence in 
Fig. 9 the crosshatched area on the diagram is a measure of 
work done. 

Change of Associated Heat during Isothermal Changes of 
Gases. 

(d) In order that a gas may expand and do work, an amount 
of energy equivalent to the work done must be supplied from 
some internal or external source. The only heat energy asso- 
ciated with an ideal gas* is that associated with it as sensible 
heat, and that stored in surrounding media as a result of previous 
expansion to the present volume. 

In isothermal expansion temperature is constant by definition, 
and since under this condition the internal energy of an -ideal 
gas is constant, it follows that there can be no change in the 
store of sensible heat of the expanding gas, and therefore that 
this store cannot be the source of energy for the doing of work. 

In any expansion the energy stored in external media is in- 
creased, and therefore this store cannot be a source of energy to 
do work, during the expansion. 

Hence a gas doing work can expand isothermally only if it 
receives from an external source an amount of energy equal to the 
work done, and this energy can only be received as heat. It 
follows, then, that an ideal gas expanding isothermally and doing 
work receives from surrounding media during the expansion a 
quantity of heat equal to the external work done, hence, from Eq. 
(43a), for any weight of gas, 

A<.= A£=^i'^'B.t.u. . . (44a) 

* It is assumed that no chemical change occurs nor any change of motion 
of the gas as a whole. 



50 HEAT-POWER ENGINEERING 

And for unit weight, 

AO=^^y|^B.t.u. .... .(44b) 

Thus during isothermal expansion there is no change of heat in 
the gas itself; the gas merely serves as a conveyor of the added 
heat AQ; and this heat may be considered as external work AE, 
in the solution of problems. Hence, during isothermal expansion 
in a piston engine the work delivered through the piston rod 
is equal to this AQ. 

(e) If a gas is forced to expand, and to do external work, with- 
out a supply of heat energy from some external source, it derives 
the necessary quantity from its own internal store of sensible 
heat; but this is accompanied by a temperature drop and the 
expansion cannot be isothermal. 

Isothermal compression is the reverse of isothermal expansion 
and the work done on the gas appears as heat, which must be 
removed as fast as it is generated ; otherwise the gas will absorb 
this energy as sensible heat, with rise in temperature, and the 
operation cannot then be isothermal. 

It may seem at first sight as if isothermal expansion of a per- 
fect gas furnished an exception to the second law of thermo- 
dynamics. It is certainly true that all the heat energy supplied 
to the gas under such conditions is completely converted into 
mechanical energy, but it is equally true that this process cannot 
continue indefinitely. That is, such a transformation cannot 
go on continuously, and must stop in general when the pressure 
of the expanding material has reached that of the surrounding 
media. 

3o» Adiabatic Volume Changes of Gases, (a) During adia- 
batic expansion or compression no energy, in the form of heat, 
is supplied to, or withdrawn from, the expanding gas, as would be 
the case if the walls of the vessel surrounding the gas were of 
material which is perfectly nonconducting as regards heat. 
Therefore all heat that is transformed into external work by 
such expansion must come from the sensible heat store of the 
working gas, and all work that is transformed into heat by such 
compression goes to increase the store of sensible heat of the gas. 

More briefly — the external work done by the adiabatic ex- 
pansion of a gas has its energy source in the sensible heat of the 



EXPANSIONS AND COMPRESSIONS OF GASES 5 1 

gas. The heat resulting from work done in adiabatic com- 
pression is stored as sensible heat in the gas. 

To illustrate adiabatic changes, imagine a gas confined in a 
cylinder permanently closed at one end and supplied with a 
frictionless piston. Assume that the apparatus is all made of 
material that will neither absorb nor transmit heat. If the pis- 
ton moves out, the volume of the gas will increase adiabatically 
and external work will be done; if the piston moves in, the volume 
will decrease adiabatically and work will be done upon the gas. 

(b) During adiabatic volume increase against resistance — that 
is, during adiabatic expansion with the doing of external work — 
the temperature of the gas must fall because external work is 
done at the expense of sensible heat. During adiabatic volume 
decrease — adiabatic compression — the temperature must rise 
because the heat equivalent of the work of compression goes to 
increase the sensible heat of the gas. Obviously, in this imagi- 
nary operation, the heat that disappears during expansion equals 
the 'external work done; and during compression the work of 
compression equals the heat increase in the gas. 

Equation for Adiabatic Changes of Gases. 

(c) The equation representing the adiabatic change of a gas 
has the form 

P7" = Const (45a) 

which may be rewritten 

PV- = PiFi" = P2F2" . . P,F." = Const. . . (45b) 

in which w = 7, as will be shown when Eq. (48) is derived. 

Work during Adiabatic Changes of Gases. 

(d) Using reasoning similar to that which led to Eq. (41), the 
expression for work done during an adiabatic change must be 

778 A£ = / PdV. 

PiFi" 
Substituting in this P = ■, obtained from Eq. (45), gives 



J'^2 dV C^^dV 



P.^^a.^-r.-~) ,,,,^ (46) 



52 HEAT-POWER ENGINEERING 

This can be simplified by performing the multiphcation indi- 
cated in the numerator, then substituting from the relation 

PiFi" = P2F2" 

and cancelling, thus obtaining for any weight of gas, 

778A£ = ^^i^^^^^ft.-lbs (47a) 

and for one pound of gas, 

778A£:= ^^^J^_~^^^^ ft-lbs (47b) 

These equations cannot be used numerically, however, until 
the value of n is known. This will now be determined. 

(e) Since the sensible heat lost by a gas when expanding 
adiabatically and doing external work must equal the work 
done, and since, in any case, the sensible heat energy lost per 
pound of a gas which is changing temperature in any way from 
Ti to a lower value T^, must equal Kv {Ti — T2) ft.-lbs., —it 
follows that 

and substituting for Kv its value from Eq. (33) 

(7 - 1) in- 1) 

from which it follows that 

« = 7 (48) 

Then the equation of an adiabatic change is, as was mentioned 
in connection with Eq. (45), 

PV = Constant (49) 

(f) The work done is, from Eq. (47a), for any weight of gas, 

778 AE = ^^1^^ I ^f' (ft.-lbs.) . . . (50a) 
and for one pound is, from Eq. (47b), 

778 A£ = ^ ^(^'-Tif '^ (ft.-lbs.) . . . (50b) 



EXPANSIONS AND COMPRESSIONS OF GASES 53 

Temperature Change of Gas during Adiabatics. 

(g) Since during an adiabatic process the stock of sensible 
heat, and hence also the temperature, is constantly changing, — 
dropping during an expansion and rising during a compression, — 
it is necessary to find some means of determining the extent of 
this temperature variation. If a gas changes adiabatically from 
PiFi to P2V2, Eq. (49) gives 

PiFi^ = P2F2- ; or ^^ = 1 .... (a) 

•and the law of ideal gases gives 

P^^Ml . or P-^ = I^. . . . (b) 
Ti T2 ' P2V2 T2 

If the last forms of expressions (a) and (b) be multiplied to- 
gether, there results 

Ti /F2V-1 ^-1 , , 

and substitution for -=-r from the first form of (a) gives 

'^ = (Sf '-^ 

Either Eq. (51) or (52) can be used for finding the tempera- 
ture resulting from an adiabatic change if the initial temperature 
is known. 

31. General Expression for Volume Changes. (a) All the 
common volume changes of gases can be represented with neces- 
sary accuracy by the general form of expression, 

PV = Constant. 

It is of course assumed that n will have a special numerical 
value for each different type of change. The truth of this 
proposition for the changes so far developed can be seen by 
writing the equations in the following fashion: 

For pressure const., P = Const, may be written PF" = Const. 
For volume const., F = Const, may be written PFoo = Const. 
For isothermal, . PV = Const, may be written PV^ = Const. 
For adiabatic, . PV = Const, is .... PV' = Const. 



54 



HEAT-POWER ENGINEERING 



(b) A comparison of the expansion curves (Fig. lo) will show 
that as the graph of the different expansions considered swings 

down through the quadrant 
BAE the exponent increases 
in size. The facts that any 
equation with n < 1 > o gives 
a graph less steep than the 
isothermal and that any equa- 
tion with w > 1 < 00 gives one 
steeper than the isothermal are 
very useful and should be 
memorized. The idea of 
steepness in this statement is 
important, as in general one 
curve cannot be said to lie 
above or below another. For 
example, if the curves in Fig. 
10 are continued as compres- 
, their relations as to vertical 





1 




D 








^ 
^ 


V-8 













't 


A C 


Dnstanb Pressure B 




1 


V 


Change n=0 f 






a 
1 


""" 




^4. 


■""ff 


vS^^ 






1 


V 


^.^^' 





Volumes 
Fig. lo. — Showing Effect of Value of n in 
Equation PV^ = Const. 

sions, to the left from the point A 
position are reversed. 



32. Construction of Lines Representing Volume Changes. 

(a) In dealing with heat engines it is frequently necessary to 
construct the lines representing graphically the changes already 
discussed and others of similar character. This can always be 
done by substituting assumed volumes or assumed pressures in 
the equation for the type under consideration, solving for the 
other quantity and plotting the resulting points. The curve 
joining these points is the graph sought. An exponential form 
of equation involves the use of logarithms and in some cases the 
calculations become a little more troublesome. 

It is 'therefore convenient to know graphical methods of de- 
termining directly the curves representing the various changes. 

Graphical Construction of Curve PV = Constant. 

(b) In Fig. II, with coordinates P and V as before, let it be 
desired to draw an equilateral hyperbola through point A. For 
doing this two methods will be given. First Method: — Draw 
through the point A horizontal and vertical lines pp\ and ViVi ; 
next, from the origin draw any number of rays (such as Od) 



EXPANSIONS AND COMPRESSIONS OF GASES 



55 



to intersect these lines (as at a and b) ; then horizontal and ver- 
tical lines drawn through these points of intersection will meet 
at points (such as B) on the desired curve. For expansion from 
point A, the rays fall below A; for compression, they fall above. 
Second Method: — Through A, Fig. 12, draw any number of 





Figs. II and 12. — Construction of Curve PV 



Constant on PV-Chart. 



lines, as bbi, cc\, etc.; make b\B = Ab, CxC = Ac and so on; 
then the points A, B, C, etc., will be on the desired curve. 



Construction of Curve PV" = Const, by Using Logarithmic 
Cross-Section Paper. 

(c) The equation PV"" = K ^ const., if solved by logarithms, 
takes the form log P = — n log V + log K. Then letting y = 
log P, X = log V, and k = log K, the last equation may be re- 
written y = — nx -\- k. This is the equation of a straight line 
with negative slope n and ^'-intercept k. It is shown in Fig. 13 
by KS, drawn to the ordinary uniform scales Ox and Oy. The 
abscissa of any point A on KS, measured on the scale Ox, gives 
the logarithm of the value of V represented; its ordinate on 
scale Oy is the logarithm of the value of P. 

If now new scales Ly and Lp are constructed in such a manner 
that the lengths 1-2 and 1-3, etc., represent the logarithms of 2, 
3, etc., — as is done on the scale of the slide rule, — then these 
logarithmic scales may be used for reading directly the numerical 
values of P and V corresponding to points on KS. To the 
scale Lp, the j'-intercept of this line is the constant K, and to 
the uniform scale the slope is n. Since the values of P and V 



56 



HEAT-POWER ENGINEERING 



^o°^^ 


P 




















9 

3 
2 




















9 






































8 


K 


















k 

1 

6 
5 


\ 


















\ 




































i 
3 
2 

1 



A 


\ 


















\ 


\ 


s 










L 



Fig. 13. — Logarithmic Chart. 



may be read directly on the logarithmic scales, the uniform 

scales are not usually given on charts of this character. 

Any straight line can be lo- 
cated on the logarithmic chart 
if the PV values for two 
points are known; or if one 
point and the slope n are 
given; but in the latter case 
it must be remembered that 
the slope is laid off using the 
uniform scale. For one of the 
points it is sometimes conven- 
ient to use the ^/-intercept, K. 
After the line has been 
JP" drawn the simultaneous values 
of P and V may be read, and 
these may then be used in 

drawing the P V curve on ordinary cross-section paper. 

The chart in Fig. 13 is arranged for numbers between i and 10, 

but it may be used for numbers between .1 and i, between 10 

and 100, 100 and 1000, and p 35 

so on, by merely changing ^^^ 

the scales to suit. 

When a wider range of 

numbers is under considera- 
tion (as from .1 to 100) a 

" checkerboard " composed of 

several similar logarithmic 

charts may be used. Thus 

in Fig. 14, let each of the 

squares contain such a chart 

and let the one surrounded 

by heavy lines correspond to 

Fig. 13, with KS reproduced. 

In the lower tier of charts 

the ordinates are for numbers from .1 to i, in the middle tier 

they are from i to 10, and in the upper from 10 to 100. The 

abscissas for the vertical columns progress, from left to right, by 

multiples of ten also. 

The coordinates of a point anywhere on the checkerboard can 



\m i 


\q 


M' S' Q' 




\ 

K 
T 




K' 
T' 


1 


U' S\ Q" 

T 
1 


10( 



Fig. 14. — Checkerboard of Logarithmic 
Charts. 



EXPANSIONS AND COMPRESSIONS OF GASES 57 

be read directly on the proper scales. For example, point B 
has coordinates P= 25 and V= .35; for point C the value of 
P is .14 and F is 13. 

As all the squares are cross-ruled the same, and differ only as 
to scales (and that by multiples of 10), it is evident that if S'T' 
is drawn in the central chart in a position similar to that of 
^T in the square below, it can be used in place of the latter line 
provided points on it are read to a scale tV that used for KS. 
Similarly, T"U', K'Q', and Q"M' may be drawn to correspond 
to TU, KQ, and QM respectively, and may be used instead of 
them with proper change in scale. Thus a single logarithmic 
chart may be used in place of the checkerboard. Obviously, 
when the curve crosses a horizontal boundary line the scale of 
ordinates changes; and when it crosses a vertical boundary the 
scale of abscissas changes. 

li n = I, as in the case of the equilateral hyperbola, the slope 
of the line is — 45°. If the exponent is greater than i , the slope 
is steeper, and vice versa. 



58 



HEAT-POWER ENGINEERING 



si 


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+ + 


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pCK^IcC 


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E^K 


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1^ ^ 


IrT ft^ 


1^ 


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II II 


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II II 


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£ 11 


fC 


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Sk ^I> 




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CHAPTER VI. 

REVERSIBILITY.* 

33. Definition, (a) Processes, or series of changes, which 
may be made to occur with materials and their associated 
energies are broadly divided into two kinds: 

1. Irreversible processes, and 

2. Reversible processes. 

An Irreversible Process is one which affects the participating 
materials and energies in such a way that after its total or 
partial completion it would be impossible to return those mate- 
rials and energies to initial conditions, without leaving changes 
in other materials and their associated energies. All the actual 
processes with which the engineer has to deal are of this character. 
It is, however, possible to imagine some of these processes as 
taking place under ideal conditions in such a way that after their 
completion everything can be again returned to starting condi- 
tions without leaving changes in anything, even though it be 
entirely extraneous to the system under investigation. Such 
ideal changes are called Reversible Processes. 

(b) A good mechanical example of a reversible change is 
furnished by a pendulum swinging on a frictionless support and 
in a perfect vacuum. Each cycle of the pendulum is accom- 
panied by a change of kinetic to potential energy, and then a 
reversal of this process so as to bring everything concerned to 
exactly the conditions pertaining at the start. This, then, is a 
process which may be said to be by nature reversible. 

A real pendulum can never reproduce this ideal process exactly, 
because of friction at the support and more or less friction in 
the enveloping medium. These resistances change some of the 
kinetic energy of the pendulum into heat which in the usual 
case leaves the system by radiation. Thus, the end of each 
cycle finds the pendulum system poorer in energy by the amount 

* The study of this chapter may be deferred until Section 49 (h) is reached. 
59 



6o HEAT-POWER ENGINEERING 

of heat which has been lost; and surrounding materials must of 
course have gained a corresponding amount of energy. The real 
process does not therefore fulfill the requirements of a reversible 
process.* 

(c) It will be observed from the preceding paragraph that the 
ideally reversible process becomes imperfectly reversible as soon 
as losses are assumed to occur. Although the process could never 
be performed in reality without such losses, this does not in- 
validate the determination of the laws of the ideal pendulum, — 
laws which are very valuable for investigations of a certain type. 
Since a reduction of losses in a real process of this character will 
cause the process to approach the ideal reversible one more 
closely, it is evident that the reversible process and the laws 
derived for it may be regarded as the ideal limiting case of 
the real process and of the laws governing it. This applies to 
processes of a certain character only. 

(d) There are many other processes of such character that 
no assumptions of ideal mechanisms and no reasonable assump- 
tions as to the elimination of losses can reduce them to limiting 
reversible processes, as was done in the case of the pendulum. 
Such processes are the irreversible ones, examples of which will 
be given later. 

(e) In the investigation of certain thermodynamic trans- 
formations accompanying pressure, volume, and temperature 
changes, it is often possible and desirable to assume all losses 
absent so that the process may be considered reversible. The 
assumptions as to the elimination of loss must be reasonable ones, 
however, — those not involving changes in the intrinsic character 
of the process. Thus it is permissible to assume that there is 
an absence of friction, and that one may use a material which 
does not conduct heat, as was done in previous chapters; but an 
assumption that there is no internal heat energy lost when a gas 
does work by expanding adiabatically behind a piston would 
have been unreasonable, as it would have been absolutely con- 
trary to the intrinsic character of the process. 

* The process might still be considered reversible if there was any way of gather- 
ing up the energy lost as heat, converting all of it into mechanical form, and return- 
ing this to the pendulum. But, even assuming that the heat could all be caught, 
the second law of thermodynamics states that it cannot all be again converted 
into the mechanical form, and the statement made above must therefore be correct. 



REVERSIBILITY 6 1 

The study of an ideal reversible process in lieu of a real im- 
perfectly reversible one greatly simplifies problems and makes 
possible the development of laws which would otherwise be 
obtainable only with great difficulty. 

(f) For thermodynamic purposes a reversible process may be 
defined as follows: 

A thermodynamically reversible process is one involving heat 
and mechanical energy transformations which are of such 
character that, after completion, they can be carried through in 
the opposite sense, without resulting in any changes in anything 
extraneous to the system under consideration. 

The practical application of this simple definition is often 
confusing. There are certain processes which are obviously 
reversible in this sense and certain others which are as obviously 
irreversible; but there are also many about which a decision is 
difficult. A few reversible and irreversible thermodynamic 
processes are given in the succeeding sections. 

34. Some Reversible Processes, (a) A good example of an 
ideal thermodynamically reversible process is as follows: Imagine 
a perfect gas inclosed in a cylinder made of material that will 
neither absorb nor conduct heat and let it be fitted with a friction- 
less piston of the same material. If the gas expands it must 
do so adiabatically, since the heat insulation is assumed to be 
perfect. The temperature will drop, the volume will increase, and 
work will be done in driving the piston outward against what- 
ever resistance is offered — for instance, the raising of a weight. 

If, after the piston has reached a certain point, the work which 
has been done by the gas is returned to drive the piston back to 
its original position — for instance, by the dropping of the lifted 
weight, — the gas will be compressed adiabatically to its original 
condition and, in the ideal case, nothing in the universe need have 
been changed by the process. 

Such a process is thermodynamically reversible. It is evi- 
dently ideal and can only be approximated in real cases, for every 
material known absorbs and conducts heat, and no piston can be 
frictionless.* 

* It is really necessary to further stipulate that the expansion and compression 
of the gas in this process take place at infinitely slow rates, to make it perfectly 
reversible in theory. This is necessary in order to exclude any degree of what is 
termed " free expansion," an irreversible phenomenon which will be treated in a 
later paragraph. 



62 HEAT-POWER ENGINEERING 

(b) Again, Imagine a body which is at a certain temperature, 
and is so arranged that the withdrawal of heat from it does not 
change its temperature. The steam in a boiler is a body of 
material approximating this conception. If a confined body of 
gas is kept in contact with this source of heat, or hot body, — ■ 
as in a steam- jacketed cylinder made of perfectly conducting 
material, — and if it is allowed to expand and do external work, 
such as driving out a piston against resistance, the expansion 
must be isothermal. During the process heat will be drawn from 
the hot body and appear as mechanical energy to do external 
work. This work may be returned by compressing the gas 
isothermally and restoring the resulting heat to its original 
source. The ideal process is thermodynamically reversible, but 
practically some heat must have been radiated and some lost 
as friction, so that the reversibility is, as before, ideal only. 

(c) A reconsideration of the simple ideal expansions discussed 
in Chapter V will now show that all of these may be made 
reversible processes. 

35. Some Irreversible Processes, (a) One of the best ex- 
amples of an intrinsically irreversible process is furnished by 
the passage of heat from one body to another which is at a lower 
temperature. Consider two bodies at different temperatures 
brought into contact and thermally isolated from the rest of 
the universe. Experience shows that the colder body will receive 
heat from that having the higher temperature, and that this proc- 
ess will continue until the two temperatures become the same; 
also it shows that certain physical changes will accompany this 
passage of heat. Thus there may be a change of state, as 
would be the case, for instance, if the colder body is ice at 
the melting point; or again, there may be simply changes in 
volume accompanying the doing of external work. 

No matter what the conditions, no method has yet been 
devised to reverse this process thermodynamically; that is, to 
make heat flow from the previously cool body to the other so 
as to leave them at different temperatures, return them to the 
initial physical conditions, and leave no change in anything 
else. The process is then irreversible by definition. 

(b) Another example of an intrinsically irreversible process is 
the free expansion of a perfect gas similar to that which occurs 



REVERSIBILITY 63 

in Joule's experiment.* Imagine two vessels of equal size 
joined by a pipe containing a valve, all made of non-heat-con- 
ducting material. Imagine further that one vessel contains a 
quantity of perfect gas at some given pressure and temperature 
and that the other vessel is absolutely empty. If the valve in 
the connecting pipe, is opened, the gas will rush from the high- 
pressure vessel into the other one and ultimately both will 
contain the same quantity of gas at the same pressure and 
temperature. To make this possible, the gas originally contained 
in one vessel must have expanded until its volume became suffi- 
cient to fill the two. Since the volume occupied by the gas is 
now greater than before, the pressure must be lower unless the 
temperature has risen, and it will be found that this has not 
occurred. Further, since the vessels and connecting pipe are 
nonconducting, and since the system is so arranged that no 
disturbance of surrounding media can be caused, it follows that 
there can have been no loss of heat energy by the gas. 

The heat energy associated with the system must therefore he 
the same before and after the change. Since, however, as was 
shown in connection with the specific heat of gases, the intrinsic 
heat energy of a perfect gas is always the same at the same 
temperature, it follows that the temperature of the gas must be 
the same when filling two vessels as when filling one. 

To make this process reversible, it must he possible to com- 
press the gas again into one vessel, keep the temperature the 
same, and have no change in anything outside the system of two 
vessels and contained gas. This is impossible, as work would 
have to be done upon the gas to compress it, and there would 
then either be a rise in temperature or the heat of compression 
would have to be absorbed by some body outside the system. 
This heat, though equal to the work of compression, could not 
be returned to the engine, or device doing that work, as an 
equivalent of the work done. This is so because (according to 
the Second Law of Thermodynamics) no engine could deliver 
in mechanical form all the heat supplied it. 

Obviously the process is intrinsically irreversible because it is 
impossible to imagine its thermodynamic reversal even with 
ideal mechanism. 

* This is not to be confused with Joule's experiment for the determination of 
the mechanical equivalent of heat. 



64 HEAT-POWER ENGINEERING 

(c) The process of free expansion is one of the most interest- 
ing and is worthy of more detailed study. What really happens 
is best considered in two parts. 

The gas in the high-pressure vessel begins to expand as soon 
as the valve in the connecting pipe is opened, and it acquires 
a high velocity with rapid drop of pressure as it flows into the 
empty vessel. The kinetic energy associated with this velocity 
must come from the intrinsic heat energy possessed by the gas. 
The expansion is in reality adiabatic, and the intrinsic heat 
energy, which during expansion behind a piston would have 
been converted into mechanical work, is here converted into 
the kinetic energy acquired by the gas itself. The temperature 
of the gas drops just as in the other adiabatic expansions already 
considered; thus, the material entering the empty vessel has 
the low temperature which corresponds to the low pressure and 
is deducible directly from the law of adiabatic expansion. 

Considering next the receiving vessel, — the gas with low 
pressure and temperature enters with high velocity but imme- 
diately becomes churned up, impinges on the walls, etc., and 
slowly comes to rest. The energy originally possessed by virtue 
of its velocity cannot be destroyed, but is reconverted into heat. 
It is absorbed as sensible heat by the gas and raises its tempera- 
ture. Given sufficient time, equilibrium will be established 
between the material in the two vessels, and then the gas, with 
the same stock of heat as before, will have returned to the tem- 
perature it had initially.* 

* The importance of the footnote on page 6i can now be appreciated. If 
gas, expanding adiabatically behind a piston, is allowed to acquire an appreciable 
velocity, some of the heat energy which has previously been assumed as doing 
external work will be used to impart this velocity to the gaseous molecules. In 
just so far as this occurs the process will be irreversible. In all real piston engines 
the velocity acquired is so small that the heat thus used is negligible. Hence no 
attention is ever given the phenomenon from this viewpoint, and it need not be 
considered in discussing the elementary cycles in the following chapters. 



CHAPTER VII. 

ENTROPY. 

36. Explanatory. In the more advanced discussions of ther- 
modynamic theory a certain property of substances, know as 
their " Entropy'' (represented by <^), is found to be of great 
importance. The solution of most, if not all, engineering prob- 
lems involving thermodynamic changes can be obtained with- 
out employing entropy; but its use enables scientists to draw 
certain sweeping conclusions with regard to natural phenomena, — 
conclusions which would otherwise be difBcult to formulate, and 
which materially assist in developing the laws governing thermo- 
dynamic transformations. The consideration of entropy also 
serves the useful purpose of giving the engineer a broader view- 
point with regard to the processes he makes use of. For these 
reasons it is introduced here. 

37. Definition, (a) It has been seen that it is impossible to 
measure the absolute amount of associated heat energy ((2), 
and that all cases can be analyzed when the discussion is limited 
to changes of energy {dQ, 8Q, or AQ) . Later it will be shown that 
entropy is a similar function ; therefore the treatment will be 
Hmited to entropy changes {dcj), 50, A</)), rather than to consider 
the absolute amount. 

(b) To a student unable to distinguish between heat and cold 
and not familiar with the phenomena accompanying tempera- 
ture changes, it would be very difificult to convey a conception 
of what a temperature change really is. Probably the best 

FtC) 
definition would be the mathematical one ST = -~^ which would 

be unsatisfactory and troublesome to the student until, by 
experience, he became familiar with the phenomena accompany- 
ing changes in temperature. The same difficulty occurs in 
attempting to define any unfamiliar physical quantity or prop- 
erty, and applies equally well to entropy. Hence, the best 

65 



66 HEAT-POWER ENGINEERING 

that can be done at present is to give a mathematical definition 
of entropy and rely on the experience and familiarity, which 
will come from the solution and discussion of problems involving 
its use, to give a more or less concrete conception of the physical 
meaning and properties. 

(c) The Mathematical Expression for an Infinitesimal Change 

of Entropy per pound of material is 

^^ dS + dl+APdV , , 

d(t> = Y ' *^53) 

in which the numerator indicates the summation of the in- 
finitesimal changes indicated, 

T = absolute temperature of material during these infinites- 
imal changes, and 

A = 1/778, introduced to keep all terms in numerator in 
same units. 

A finite change of entropy per pound of material will then be 

^^ nds-\-di+ APdv , - 

For W pounds this becomes 

A«A = W^^ T^ . . . . (55) 

(d) It will be observed during the further development of 
thermodynamic phenomena that all those processes which occur 
" naturally," i.e., spontaneously, are accompanied by an increase 
of entropy. Any process which results in a decrease of entropy 
must be forced in some way, and is in that sense " unnatural." 
Hence it may be said that the entropy of every substance tends 
to increase. 

A somewhat analogous, though not a parallel, case may be 
cited from mechanics. It is well known that the potential 
energy of mechanical systems always tends to decrease, for 
there is a tendency for the centers of mass of all terrestial bodies 
to approach the earth's center as closely as conditions will 
permit. Given a mechanical system, in which processes result- 
ing in change of the position of the center of gravity can take 
place, that change will occur which will make the potential 
energy of the system least, unless external forces impose a 
different behavior. 



ENTROPY 67 

38. Entropy Changes for Reversible Processes with Ideal 
Gases, (a) It was mentioned (in Section 34c) that the ideal 
expansions considered in Chap. V may be made reversible proc- 
esses; and a further consideration will show that in every 
such case the external work, dE, can be represented as AP dV. 
Further study will show that for all reversible processes 

APdV = dE and A C P dV = AE. 



s: 



Then, since dl = o for an ideal gas, the numerator of Eq. (53) 
becomes dS + dE = dQ. And the^ infinitesimal entropy change 
experienced by unit weight of ideal gas, during a reversible 
process, is then 

^^^dS + 4E^<lQ (56J 

The finite change for unit weight is 

-*=rf <^^' 

and for any weight, W, 

A4>=w£§ (58) 

(b) It must be particularly noted that the last three equations 
apply to reversible processes only, and for the present they will 
be considered as applicable only to ideal gas. They may be 
used for finding the entropy change experienced by a given 
weight of ideal gas which, while expanding behind a piston, is 
undergoing one of the reversible processes, such as those de- 
scribed in Chapter V; they are not applicable for determining 
the entropy change when a given weight of gas experiences an 
irreversible process, such as the free expansion of Joule's experi- 
ment, Section 35 (b). In such cases the entropy change must 
be determined in other ways which will be presented later. 

39. Sign of Entropy Changes during Reversible Processes. 

(a) The integration of Eq. (57) between the limits i and 2 for 
any assumed process will result in a difference of two quantities; 
thus the sign of the right-hand member will depend upon which 
of these quantities is the larger. The sign of this number indi- 
cates whether the process in question will increase or decrease 
the entropy of the material. 



68 HEAT-POWER ENGINEERING 

(b) A reversible increase of heat energy would give a positive 
value for the right-hand member of the equation, — a positive 
value of A(^, — and this corresponds to an increase of entropy. 

(c) A reversible rejection of heat results in a negative Value 
of A0, indicating a decrease of entropy. 

(d) Eq. (57) would show no change of entropy for any revers- 
ible process involving no change of associated heat, but this 
could only be true of an adiabatic process (in which dQ = o, see 
Section 30 (a) ). An ideal gas, therefore, experiences no change 
of entropy during a reversible adiabatic process. 

(e) Although it is the entropy change which is really con- 
sidered in thermodynamic calculations in which entropy is con- 
cerned, yet engineers are accustomed to speak of the " total 
entropy " of the substance for the particular conditions of tem- 
perature, pressure, and volume pertaining. They do this because 
they have by common consent agreed that the entropy of 
materials shall be measured above a certain arbitrarily chosen 
datum, which is taken as zero for convenience. Thus the term 
" total entropy " (<^) refers to the total entropy change ex- 
perienced by the material in passing reversibly from the arbi- 
trarily chosen datum to the conditions in question. As the 
entropy difference (<^2 — ^1) is dealt with, any datum whatever 
may be selected provided the same one is used for both of the 
entropy quantities, 02 and 0i. 

40. Entropy Changes during Reversible Isobarics of Gases. 

In Eq. (56) the numerator of the right-hand member can be 
replaced by the product of specific heat into an infinitesimal 
temperature change, thus 

,i. = f = ^, (59) 

the symbol C representing the proper specific heat for the par- 
ticular change under consideration. 

For a change at constant pressure C becomes Cp and the 
differential equation for entropy change is 



(60) 



Assuming Cp a constant as before, the total change of entropy 
is, per unit weight, 

£d<i>=Cp£^ (6ia) 



ENTROPY 69 

Thus A(^ = (02 - 0l) = Cj, (loge T2 - \0ge ^i). . (6lb) 

= C, log/^ (6ic) 

Eq. (61 b) or (6ic) will Indicate by the algebraic sign of its 
right-hand member whether a positive or negative entropy 
change is under consideration. Increase of associated heat will 
make T2 greater numerically than Ti and the right-hand mem- 
ber of the equations will then have a positive sign, which 
indicates an increase of entropy. Reduction of associated heat 
will make T2 less than Ti and the right-hand member of the 
equations will have a negative sign. 

The equations can then be trusted to give not only the numeri- 
cal value of the entropy change, but also to signify whether it 
increases or decreases the total entropy of the material under 
consideration. 

41. Entropy Changes during Reversible Isovolumics of Gases. 

In this case the specific heat C in Eq. (59) becomes Cv and the 
resulting differential equation is 

d* = ^ (62) 

The total change of entropy is, therefore, per unit weight, 

or A0 = (02 - 0i) = C, (log, T2 - log. Ti). . . . (63) 
= C.log.p^ (63a) 

As before, the algebraic sign of the right-hand member of this 
equation will indicate whether an increase or decrease of entropy 
is under consideration. 

42. Entropy Changes during Reversible Isothermals of Gases. 

During an isothermal change the temperature is constant by 
definition; that is, T in Eq. (56) is the same for each of the differ- 
ential heat changes dQ. Then 

dQ 
T 

* It is usually more convenient to use logio instead of logg. As loge = 2.302 logio, 
Eq. (6ic) may be written A0 = Cp X 2.302 logio (Ti/Ti). The other logarithmic 
equations which are to follow may be similarly transformed. 



J ^2 r2 



70 HEAT-POWER ENGINEERING 

becomes 

A0 = (02 - 0i) = ^^^-^ (64) 

Thus, for isothermal changes, since {Q2 — Qi) = AQ, 

A« = f (65) 

The entropy change will obviously have the same sign as AQ, 
indicating increase of entropy with increase of associated heat 
and decrease of entropy with decrease of associated heat. 

43. Entropy Changes during Reversible Adiabatics of Gases. 

An adiabatic change being one which occurs under conditions of 
heat insulation, that is, one during which heat energy is neither 
given to nor abstracted from the substance, it follows that 
dQ = o, and therefore 

^^ = ^ = 0.. (66) 

Thus during a reversible adiabatic change there is no entropy 
change, just as during an isothermal process there is no tem- 
perature change. Reversible adiabatics are therefore often called 
Isentropics, and these two terms may be used interchangeably. 

44. Irreversible Adiabatic Processes of Ideal Gas, and the 
Corresponding Entropy Changes, (a) Besides the reversible 
adiabatic expansion already discussed, there are an unlimited 
number of adiabatic processes which are irreversible. These 
are thermodynamic processes which ideal gas undergoes when 
confined in vessels which are nonconducting as regards heat, 
that is, in those which neither permit the gas to receive nor to 
surrender any heat through the surrounding walls. Of the 
processes which are strictly adiabatic, those which are isentropic 
are the only ones that are reversible. 

(b) As an example of an irreversible adiabatic change of ideal 
gas, assume the process similar to the free expansion of Joule's 
experiment, discussed in Section 35 (b). During such a process, 
the entropy change experienced by unit weight of gas cannot 
be found by Eqs. (56) and (57), as they apply only to reversible 
processes. An attempt to use them would give the zero entropy 



ENTROPY 71 

change that was obtained in Section 43, which is very far from 
being correct, as the next paragraph will show. 

(c) Recourse must then be had to the original definition, 
Eq. (53), which may be rewritten as 

dct) = J, [-A-Y- (a) 

In the process under discussion there can be no change in the 
sensible heat because the temperature of the gas is the same after 
as before the- change, and dl is of course zero for ideal gas. 
Hence dS -\- dl = o and Eq. (a) becomes 

d,^A^ (b) 

The PVT changes in a unit weight of ideal gas are represented 
by the expression 

Thus P = RT/Y 

and PdN = RT^-- 

This value of PdY may now be substituted in Eq. (b), which 
then becomes 

,RTdV , RdV 
d4> = A^^ -=A-^. 

Integrating this between the limits i and 2 gives the true entropy 
change, per pound of material, 

A0=^j^ i?^=^i?(log,V2-log«Vi). . . (c) 

As the volume V2 occupied when the gas fills the two vessels 
is greater than the volume Vi which it had when confined in one 
of them, the process, as shown by Eq. (c), must result in an 
increase of entropy despite the fact that the conditions are 
adiabatic. This is quite different from the zero value obtained 
by applying the equation for reversible changes in which APdV 
= dE. This emphasizes the statement already given that only 
reversible adiabatics are isentropic processes. 

(d) The free expansion of a gas may be called a " natural " 
process. It was seen to be accompanied by an increase in 



72 HEAT-POWER ENGINEERING 

entropy of the materials concerned. A similar increase also 
occurs with all other natural processes, such as the flow of heat 
from a higher temperature body to one at lower temperature. 
Thus the entropy of all substances always tends to increase. 
These facts will become more apparent as the subject is developed. 

45. Entropy Changes Independent of Path, (a) The in- 
tegration of Eq. (54) results in a difference in two quantities, 
the values of which depend merely on the conditions of the 
substance before and after the change. Evidently, then, the 
entropy change is in no way dependent on the method of changing 
from the one set of conditions to the other. Thus the entropy 
change experienced by a material in passing from some definite 
set of conditions i to another definite set 2 will always be the 
same, no matter what path is pursued on the graphical repre- 
sentation of the process. 

(b) This fact is often of great importance, as the entropy 
change experienced by a substance when undergoing any very 
complicated set of changes can be determined by finding the 
entropy change accompanying any simple change, or group of 
changes, which will carry the body from the same initial to 
the same final conditions. It is, however, very essential to 
make sure that the final conditions are the same in both cases, 
as mistakes are easily made in just this point. 

46. Temperature-Entropy Diagrams, (a) Just as pressure- 
volume diagrams are useful as a means of graphically represent- 
ing certain changes, so diagrams with absolute temperature 
plotted vertically and entropy change plotted horizontally are 
capable of visualizing some very important transformations. 
They are known as T(/)-diagrams. 

There is a peculiarity about the plotting of diagrams with 
temperature and entropy coordinates, to which attention should 
be called. In the PV-diagram the intersection of the coordi- 
nate axes represents zero pressure and zero volume, and this 
is possible because both absolute pressure and absolute volume 
can be determined. In the Tc^-diagrams, however, although 
absolute temperature can be determined inferentially, as pre- 
viously shown on p. 30, the absolute quantity of entropy is inde- 
terminate like the absolute quantity of associated heat. As 
already shown, the equations give change of entropy, A0, and not 



ENTROPY 



73 



absolute giiantity of entropy, (f). It is this A0 which is used in 
plotting. The abscissas thus represent entropies of a substance 
above some conveniently chosen datum, such as that at 32° F. 

(b) In Fig. 15, the point A represents the temperature- 
entropy conditions of a substance as Ticjyi. This means that at 
temperature Ti the entropy of the substance is 01, above what- 













<^V^ 


D 
/ 

B 


G 






A 




^ 


y 


I c 


^ 


i^ 


1 
1 


Tic^i 


Isothermal 




i 

Enti 


3py 




V 


1 







Fig. 15. — T<^-Curves for Gases. 

ever value has been decided on as zero of entropy, — just as in 
the PV-diagram, Fig. 6, V\ represents the volume of the sub- 
stance above absolute zero of volume when its pressure is Pi. 

Isobaric Changes. 

(c) The line AB, Fig. 15, represents the temperature-entropy 
changes of a gas expanding at constant pressure, or it is the graph 
of Eq. (61), and is obtained by substituting various increasing 
values for Ti. Similarly, the line ^ C is the graph of a constant- 
pressure compression. 

Isovolumic Changes. 

(d) The line AD represents a rise of pressure at constant 
volume and is obtained by means of Eq. (63) ; while the line AE 
is the same curve continued backward, and represents a con- 
stant-volume pressure drop. 

Isothermal Changes. 

(e) During an isothermal change T is constant but entropy 
becomes greater as associated heat increases, which occurs as 
volume grows larger. The graph of an isothermal expansion 



74 HEAT-POWER ENGINEERING 

from 2"i0i must then be a horizontal line to the right of A ; and 
similarly an isothermal compression must be shown by the hori- 
zontal line to the left. 

Adiabatic Changes. 

(f) The entropy change is zero during a reversible adiabatic 
change, therefore A</> equals zero, and such a change must be 
shown by a vertical line on the T(/)-diagram. Further, since the 
temperature of a gas decreases during adiabatic expansion, as 
previously shown, the line A H must represent such an expansion 
from Ti(t)i conditions, and the line A I a. similar compression 
from the same point. 

Area equivalent to AQ. 

(g) From Eq. (56) dQ = Tdtf), for reversible processes, and 
hence for such a process, 

rdQ = r Td<i>, 
and A(2 = (22 - <2i = r 'rdci>. . . (67) 

The last term of this equation is, however, the mathematical 
expression for the area under a curve drawn to ^^-coordinates. 
It therefore follows that area on the T4>-diagram represents 
heat change during reversible processes, and inspection of the 
graphs already given will show that area under a line traced from 
left to right represents heat given to a substance, while area 
under a line from right to left represents heat abstracted from 
a substance. 

One of the great conveniences resulting from the use of the 
T0-diagram in engineering may now be seen. The FV-diagram 
shows by the area beneath the expansion line the total external 
work associated with a process; while, for reversible processes 
at least, the T^-diagram shows by the area beneath the corre- 
sponding line the change of total associated heat occurring during 
the same processes. The engineer is thus enabled to quickly 
solve many problems by simple inspection of these two dia- 
grams, and can avoid the necessity of making long mathematical 
calculations with the ever-present possibility of error. 

It may be objected that it involves more work and time to 
construct the necessary diagrams than it would to make the 



ENTROPY 75 

calculations direct. It will, however, be discovered in a later 
chapter that certain standard diagrams can be constructed for 
the solution of by far the larger class of problems in which the 
conception of entropy change is particularly helpful. These 
diagrams, once constructed, can be used indefinitely without 
further calculation. 



CHAPTER VIII. 

GAS CYCLES. 

47. Definition of a Cycle, (a) As already stated, man re- 
quires far more energy than his body can supply, and this energy 
is obtained from Nature's stores. Energy as used by the engi- 
neer is always associated with some substance, body, or " sys- 
tem ": kinetic energy with moving masses; potential mechanical 
energy with masses by virtue of position ; heat, sensible or latent, 
with solids, liquids, or gases. 

(b) When energy is used for the doing of work the material 
with which it is associated is called the working substance. Thus 
in a hydraulic power plant, water is the working substance; gas 
is the working substance in a gas engine; and water is the working 
substance in a steam engine. 

(c) If a given quantity of a working substance, with its asso- 
ciated energy, be used so as to obtain all the work possible under 
given circumstances, the same amount of work cannot be again 
obtained under the same circumstances unless the substance is 
first returned to its initial condition. Thus a pound of water 
falling a given distance will develop a certain amount of work, 
and that work will be the greatest obtainable under the circum- 
stances when the water falls to the lowest possible point. To 
again develop the same amount of work with the same pound 
of water, it must first be raised to the height from which it origi- 
nally fell. Or similarly,, if one pound of gas does work by ex- 
panding adiabatically from a temperature Ti to a temperature 
To, which is the lowest possible under the conditions, it cannot 
again do the same amount of work in the same way until its 
temperature is again raised to the initial value Ti. 

(d) In order to deliver work continuously as is generally 
required, there are obviously only two possible methods of 
operation: either (i) the working substance must be periodically 
returned to initial conditions, or (2) new quantities of working 

76 



GAS CYCLES 77 

substance must be supplied at regular intervals. The latter is 
the simpler and is often used, but it is not Nature's method. If 
man uses falling water to develop power and allows the water 
to run to waste at the lower level, Nature immediately begins to 
lift it by evaporation, so that sooner or later it will be again 
available. If man burns carbon in air, getting hot CO2 and N2, 
and then, after obtaining work by lowering the temperature, 
discharges the gas as useless, Nature through the agency of plant 
growth decomposes the cold CO2 into C and O2 so that they can 
again be combined to evolve the same amount of heat energy 
as before. 

Thus without man's agency all working substances periodically 
return to the same starting conditions, that is, pass through 
cycles. 

A cycle is any series of operations which periodically brings the 
working substance back to initial conditions. 

It is customary to speak of Open and Closed Cycles, but there 
are really no open cycles in engineering. If the engineer carries 
a working substance through any series of changes which does 
not return it to initial conditions, Nature kindly closes the cycle 
for him. 

(e) One difficulty here confronts the beginner: Experience 
shows that it requires at least as much energy to pump water 
between levels as can be obtained from it in flowing down again ; 
this being true, how is man to obtain available work from a 
substance if equal work has to be returned to raise the material 
to starting conditions? There are two solutions which amount 
to the same thing in the end: 

1 . Allow Nature to do the pumping, as in the case of the water- 
fall; or 

2. Imitate Nature in finding some way of pumping that does 
not require the return of the identical energy which has been 
obtained from the cycle. 

When a heat engine is used heat energy is available but mechani- 
cal energy is sought. Most of the methods in use for returning 
the working substance to initial conditions in such cases depend 
upon the use of a small amount of the generated mechanical 
energy and a large amount of the available heat energy for this 
purpose; or they employ some group of processes which are the 
substantial equivalent of this. 



78 



HEAT-POWER ENGINEERING 




48. Diagram of a Cycle. (a) Cycles are conveniently rep- 
resented diagrammatically, as has already been done for pres- 
sure-volume changes or temperature-entropy changes. The 
coordinates used are generally either P V, or Tcf). 

Assume for instance that the point A, in Fig. 16, represents 
the pressure and volume conditions PiVi, at temperature Ti, 

of one pound of gas used as a 
working substance in a cylinder 
fitted with a frictionless piston, 
as shown in the figure. If the 
gas expands to conditions P2V2 
at B, according to such a law 
that AB 'is the graph of pres- 
sure-volume changes, the area 
ABEF must measure the ex- 
ternal work done upon the pis- 
ton while it moves from position 
a to position h. If the gas then 
expands further according to 
some other law BC so as to 
arrive at the point C with con- 
ditions P3V3, the additional ex- 
ternal work done upon the piston 
while moving from h to c must be 
represented by the area BCGE. 
By compression the working substance may then be brought to 
some conditions P4V4 according to the law represented by the 
graph CD while the piston moves from c to d, but, to do this, 
work represented by the area CDHG must be done by the piston 
upon the gas. From point D compressing in the proper way will 
bring the working substance to starting conditions at A, with an 
expenditure of work shown by the area DAFH. The return of 
the gas to starting conditions at A completes a cycle; the pres- 
sure, volume, and temperature of the gas are again PiYiTi and 
the piston is back to position a. There is then no reason why 
the same process may not be repeated again and again indefi- 
nitely. Observe, however, that the total external work done by 
the gas is 

Positive Work = ABEF + BCGE = ABCGF ft.-lbs., 



d' b 

Fig. 16. — PV-Diagram of Cycle. 



GAS CYCLES 



79 



while the total work done upon the gas is 

Negative Work = CDHG + DAFH = CDAFG ft.-lbs. 
leaving 

Net or Available Work = ABCGF - CDAFG 
= A BCD A ft.-lbs. 
= A rea inclosed by lines of cycle. 

(b) Four successive processes as represented by the four lines 
in Fig. 1 6 are not necessary for a working cycle. Any number 
of processes between an infinite number and two may inclose 
an area and therefore could represent a cycle delivering work. 
Four lines are, however, employed in most of the cycles used in 
ordinary heat engines. 



49. The Carnot Cycle for Gases, (a) This cycle, named from 
Sadi Carnot, the man who first investigated it, represents the 
best that can possibly be done in the conversion of heat energy 
into mechanical energy.* It cannot be used in any actual 
engine and is therefore only of theoretical interest as a criterion of 
the maximum result obtainable. 

(b) For performing such a cycle with gas it is necessary to have 

1. The gaseous working substance; 

2. Certain apparatus, to be specified below. 

The working substance may be any gas far enough removed 
from its point of liquefaction to 
sensibly obey the laws already 
developed for perfect gases. 

The necessary apparatus is 
shown in Fig. 17 and may be de- 
scribed as follows: 

t/ is a body at high tempera- 
ture Ti and so arranged that this 
temperature remains constant de- 
spite withdrawal or addition of 
heat energy. An ordinary fur- 
nace with a controllable fuel and 



T2 



Fig. 17. 



Machinery of Carnot 
Engine. 



* This statement must not be interpreted to mean that no other cycle can do 
as well; it means only that no other cycle can do better. It will be shown later 
that there are a number of cycles equally efificient as energy transformers. 



8o 



HEAT-POWER ENGINEERING 



air supply approximates these conditions. The body U will 
hereafter be called the Hot Body. 

X is a body at temperature T2, lower than Ti, and this tem- 
perature T2 remains constant despite addition or removal of 
heat energy. A vessel jacketed with flowing water at tem- 
perature T2, or arranged like the condenser shown in Fig. 3, 
would approximate these conditions. The body X will here- 
after be called the Cold Body. 

F is a cylinder, Z is a removable plate which may be used to 
cover the end of the cylinder, and F2 is a frictionless piston. 
These parts are made of material that will neither absorb nor 
conduct heat. Fi is a cylinder head made of material that 
offers no resistance to flow of heat. 



der F at conditions Pa^a and Ta 



Operation of Carnot Engine. 

(c) Imagine first that one pound of gas is inclosed in the cylin- 

as shown at a in Fig. 18, Ta 
being equal to Ti, the tem- 
perature of the hot body. 
(i) Remove cover Z, apply 
the hot body to the conduct- 
ing head Fi, and allow the 
gas to expand isothermally to 
some lower pressure Pb at 
volume Vb as shown at h in 
the figure. The necessary 
heat supply must have come 
from the hot body and may 
be called A<2i. 

(2) Next remove the hot 
body, apply the nonconduct- 
ing cover Z, and allow the 
gas to expand adiahatically 
until its temperature has 



a 














I 












ll 












^mt 












( ' ~iM 


k 












&' 







f 




1 


^ 


"Jll ,1 


^. 



Fig. 18. — PV-Diagram of Carnot Cycle. 



dropped to Tc, equal to T2, the temperature of the cold body. 
The gas will then have conditions Pc^c- 

(3) Again remove the cover Z, apply the cold body X, and 
drive the piston back, compressing the gas isothermally to some 
higher pressure Pd at volume Yd- (The value of Pa will be con- 



GAS CYCLES 8 1 

sidered in the next paragraph.) The heat generated must be 
absorbed by the cold body and may be called AQo. 

(4) For the fourth and completing operation, remove the 
cold body, replace the nonconducting head Z, and drive the piston 
back, compressing the gas adiahatically until its temperature has 
again risen to that of the hot body, which was the starting 
temperature of the cycle. To close the cycle, the pressure and 
volume must return to Pd^fa when Ti is reached. This can only 
be attained if the isothermal compression is stopped at such a 
point d that the subsequent adiabatic compression will return 
the gas to the starting conditions. 

Work Developed by Carnot Engine. 

(d) The area crosshatched upward from left to right in Fig. 18 
represents work done hy the gas, while that crosshatched down- 
ward from left to right represents work done upon the gas. The 
foot-pounds of net work resulting from one cycle is shown by the 
inclosed area ahcd. If this cycle is carried through n times per 
minute, the total net work done by the gas will be n times the 
area abed. The mathematical expression for net work done per 
cycle can be obtained by using the formulas already developed 
for isothermal and adiabatic changes. The results are tabulated 
below. 

Before consulting this table, however, note that this cycle 
consists of two isothermals joined by two adiabatics. The 

Ti isothermal is an expansion with ratio — = r, and the T2 

* a 
Vc 

isothermal is a compression with ratio =7^ = r' . These two ratios 

Yd 

must be equal because by Eq. (51) 

Yc Ya V, V. 

so that r = r'. 

By means of the last equation the tabulated results give simple 
expressions for net work as indicated below the table. 



82 



HEAT-POWER ENGINEERING 



Line. 


Kind. 


Heat Received 
(Ft.-lbs./lb. gas). 


Work Done 
(Ft.-lbs./lb. gas). 


ab 
be 
cd 
da 


Isothermal 
Expansion 

Adiabatic 
Expansion 

Isothermal 
Compression 

Adiabatic 
Compression 


+ RT, loge r 

- RT2 loge (r' = r) 



+ RTi loge r 

- RT, log, {r'~ r) 

y - 1 



Net Work = RTi log^ r - RT2 loge r' 
= {Ti-T2)Rloger ft.-lbs. 



(68) 



Efficiency of Carnot Engine. 

(e) Efficiency is defined as the ratio of useful result to expendi- 
ture or effort made to obtain that result. That is 

^rr • -cr RcSult 

Efficiency = £/. = g^. 

The result obtained from the operation of this Carnot engine 
is the net work done hy the gas and the expenditure made is the 
heat supplied hy the hot body. Then 

Foot-pounds represented by abed 
B.t.u. represented hy area abed 



Ef. Carnot Cycle 



A(2i 



-. (69a) 
(69b) 



The heat supplied per unit weight of gas is A(2i = RTi loge r 
foot-pounds and the net work is given by Eq. (68). Hence: 

Net Work {T, - T^) R logef Ti - T-, 



Ef- = 



(69c) 



Heat Supplied TiR loge r Ti 

Objection is often made to the expressions of efficiency just 
developed because it seems as though the engine ought to be 
credited with the heat given to the cold body. The fallacy of 
this appears when it is understood that the heat given to the 
cold body leaves the engine at a low temperature, T2, whereas to 
operate the engine heat must be available at a high temperature 
Ti. The heat rejected to the cold body could not, therefore, be 



GAS CYCLES 



83 



directly used again in the engine,* and hence should not appear 
in the expression for efficiency. 

(f) To make this heat availat)le again for use in the same 
engine, it would have to be raised to the high temperature Ti and 
be returned to the engine by way of the hot body at that tem- 
perature, but experience shows that heat will not flow of its own 
accord from any body to one at a higher temperature. From the 
discussion which follows, it will be seen that at least as much 
mechanical energy would he consumed in causing such a flow as 
coidd he obtained hy using the elevated heat in a heat engine. It 
will be discovered that this is all in accord with the Second Law 
of Thermodynamics. 

The case is analogous to that in which water leaving a water 
wheel is pumped again to the original height in the attempt to 
utilize the energy still possessed by the water when leaving the 
wheel. Obviously, in this case the energy leaving the wheel 
with the effluent water is of no further use to that wheel, and 
exactly the same thing is true of 
the heat energy leaving the engine. 

(g) Fig. 19 is intended, to show 
the energy changes of the Carnot 
cycle graphically. If vertical dis- 
tances between heat reservoirs Ti 
and T2 in the figure represent tem- 
perature, and widths of streams 

represent quantities of energy, the -i aq^ 

sense of the foregoing discussion '^■ 

becomes graphically evident. '""'"" „ 1-, • ^ . 

, , r , _ Fig. 19. — Energy Flow in Carnot 

The dotted part of the figure Engine. 

shows how a part of the effluent 

energy might be used if another cold body with temperature Tz, 

lower than T'2, could be obtained. f The ultimate limit to this 



_^Q 




Work=_7jr8AE 
- -Ffc-Lb. 



* In a real case the hot body would derive the heat to maintain its temperature 
from some form of fuel, and the cost of that fuel would be the expenditure made to 
obtain the work delivered by the engine. 

t The possibility of the existence of cold body Tz immediately suggests the use 
of only one engine operating between temperatures T\ and T^. There is no theo- 
retical objection to this, but sometimes when analogous schemes are tried with 
real engines a number of practical considerations dictate the use of several engines 
in series as above, rather than one engine working through the entire temperature 
drop. The reasons will be considered later. 



84 HEAT-POWER ENGINEERING 

arrangement would be an engine having a cold body with tem- 
perature at absolute zero. 

It is of interest to note that in this limiting case the Second Law 
of Thermodynamics would no longer be true because the last engine 
of the series would reject no heat, having reduced the temperature 
of its working substance to absolute zero. All the heat entering 
the group of engines could then be completely and continuously 
converted into mechanical energy. It is obviously an impossible 
proposition, arising in this case from the impossible ideal gas, the 
assumptions made as to the properties of that material, and the 
absurd assumption that any body can be maintained indefinitely 
at absolute zero of temperature without the expenditure of 
work in a continuous process of refrigeration. 

From Fig. 19 

A(22 + A£ = A(2i; (70) 

hence the efficiency might be written, 

^^- A(2i A(2i • • • • (71) 

and this will be found to express the efficiency of any heat-engine 
cycle. From Eqs. (69c) and (71) it is evident that in the case of 
the Carnot engine with gaseous working substance 

AQi - A(22 _ T,-T, 

A(2i ~ T, ^^^^ 

Reversibility of Carnot Engine. 

(h) Each part of the process carried on in a Carnot engine is 
thermodynamically reversible. In fact the cycle is made up of 
the two. processes which were cited in Section 34 (a) and (b) as 
typical examples of reversible processes. The entire cycle must 
therefore be reversible ; that is, it must be possible to operate 
the engine starting at the point a in Fig. 18, and following the 
cycle backwards in the direction adcb. 

There is no reason why the gas cannot (i) expand adiabatically 
from a to d and then (2) isothermally, at temperature T2, from 
d to c. During the latter process it would absorb heat AQ2 from 
the cold body. If the necessary mechanical energy is available 
the gas can be (3) compressed adiabatically from c to b, and then 
(4) isothermally in contact with the hot body to the starting 
point. During the isothermal compression the gas must give to 



GAS CYCLES 85 

the hot body the amount of heat A(2i exactly equal to that previously 
removed during the direct operation. 

In the diagram (Fig. 18) the work done by the gas during 
the two expansions must be represented by the area adcef, and 
that done on the gas during the two compressions must be shown 
by the area ecbaf. The net result must then be the absorption 
of external work equal to that given out in the direct cycle and 
represented by the area adcb. Tabulation of the results of 
operation, first direct and then reversed, gives 

Direct Operation. Reversed Operation. 

Heat absorbed from hot body = AQi = Heat delivered to hot body. 

Heat discharged to cold body = AQ2 = Heat absorbed from cold body. 

Mechanical energy deHvered = (AQi— AQ2) =Mechanical energy absorbed. 
Thus the Carnot engine reversed can remove heat at low 
temperature from the cold body and, having absorbed a certain 
quantity of available mechanical energy, can deliver the sum of 
these two energies to the hot body as heat at high temperature. 
Jt is therefore a heat pump. 

Carnot Engine as a Source of Perpetual Motion of 
Third Type. 

(i) Imagine now two Carnot engines exactly alike, one working 
as an engine, and the other, with operation reversed,. working as 
a " heat pump." The engine will remove heat from the hot 
body, deliver a part of it as mechanical energy, and discharge 
the remainder to the cold body. The pump will absorb from 
the cold body the same quantity of heat that this latter received 
from the engine; it will require for its operation the same quantity 
of mechanical energy that was delivered by the engine; and it 
will discharge to the hot body the sum of the two energies, — 
that is, an amount of heat equal to that which the engine removed 
from the hot body. If the two pieces of apparatus can be con- 
nected so that the engine drives the pump, a device results which, 
theoretically devoid of friction and radiation losses, can go on 
moving forever, though delivering no useful work. This is what 
was called in Section 9 perpetual motion of the third type, 
which, though conceivable, cannot be materialized. 

50. All reversible engines have the same efficiency as the 
Carnot engine when working between the same temperature 
limits. 



86 



HEAT-POWER ENGINEERING 



There are many possible types of reversible and irreversible 
ideal engines. It will now be proved that, when working between 
the same temperature limits, — i.e., receiving heat from a hot 
body at the same temperature as that supplying the Carnot 
engine and rejecting heat to a cold body at the same tempera- 
ture as that used with the Carnot engine, — (i) no engine what- 
ever can have higher efficiency than the Carnot engine and (2) the 
efficiency of all reversible engines equals the efficiency of the Carnot 
engine. 

To prove (i): Assume that any engine. A, is more efficient 
than the Carnot engine, C. Obviously A could deliver more 
mechanical energy than could C, although receiving the same 
amount of heat; and the heat rejected by A to the cold body 
would evidently be less than that delivered by C by an amount 
equal to the difference between the quantities of mechanical 
energy delivered by A and C* 

Let Ay operating as an engine, drive C reversed, that is, as 
a heat pump. This is shown diagrammatically in Fig. 20, in 




AQ =AQ,— A ErAE. 



AQ'2=AQ„+AEj 



Fig. 20. — Heat Flow Diagram to show that no engine can 
have a greater efSciency than the Carnot. 



which the width of stream is supposed to be a measure of the 
energy flow. From the combination there would result an 
excess of mechanical energy AE2 which could be used outside 

* Because heat received = heat discharged + mechanical energy delivered. 
With the left member of the equation constant, neither term of the right member 
can vary except at the expense of the other. 



GAS CYCLES 87 

the system. This excess mechanical energy would be exactly 
equal to the only heat supplied the system, that is, to AE2 given by 
the cold body. Therefore the combination could continuously 
convert into mechanical energy all the heat supplied it ; but this 
would be Perpetual Motion of the Second Type, and is contrary 
to human experience as expressed in the Second Law of Thermo- 
dynamics. Since the assumption that A is more efficient than 
C results in this impossibility, it follows that that assumption 
must be incorrect, and that no heat engine, reversible or irrevers- 
ible, can have an efficiency greater than that of the Carnot 
engine. Hence statement (i) is correct. 

To prove (2), that if the engine A is reversible it must have 
the same efficiency as the reversible Carnot engine C working 
between the same temperature limits, imagine it to have an 
efficiency less than that of C* Being reversible, it can be used 
as a heat pump driven by C. Then, if the pump can be less 
efficient than the engine, perpetual motion of the second type 
again appears. Hence, neither engine can be more efficient than 
the other, so the efficiencies of all reversible engines working 
between the same temperature limits must be the same, which 
proves (2). 

51. Comparision of Carnot Engine and Real Engine. The 

Carnot engine as described above is evidently only an ideal 
mechanism, for the material assumed for the parts does not 
exist and a perfect apparatus could not be constructed. It is 
possible, however, to approach such ideals and they may there- 
fore be regarded as limiting cases for actual constructions. 
Comparing the real engines with the Carnot as a standard gives 
a measure of the perfection of attainment. 

In any actual engine, the piston, which itself meets with 
frictional resistance, is connected to a friction-burdened mech- 
anism. In the real engine, provision must also be made for 
storing part of the energy delivered during the expansion, to be 
returned for the compression of the working substance, and this 
storage and return always involves waste. In the reciprocating 
engine, for instance, this energy-storing device is usually a fly- 
wheel, and some of the energy stored is lost in friction and 
windage. 

* It has already been proved that its efficiency cannot be greater than that of C 



OS HEAT-POWER ENGINEERING 

Obviously there must be the following losses in any real engine: 

1. Some of the heat received from the hot body must be lost 
as heat through conduction and radiation by the material of the 
engine. 

2. Some of the mechanical energy delivered to the piston 
must be lost by friction in the mechanism of the engine. 

3. Some of the energy stored for compressing the working sub- 
stance must be lost by friction during its storage and its return. 

Recalling the meanings of the three types of perpetual motion 
(page 7), it is evident — 

(a) That no ideal engine can give perpetual motion of the first 
or second type; 

{h) That any ideal reversible engine combined with another of 
similar character can give perpetual motion of the third type only; but 

(c) That no real engine can give perpetual motion of any of the 
three types. 

52. T^-Diagram of Carnot Cycle, (a) The Car not cycle, 
being made up of two reversible isothermals and two reversible 
adiabatics, must be represented by a rectangle when drawn to 
T0 coordinates. Such a diagram is given in Fig. 21, in which 
the horizontal lines ab and cd represent the reversible isothermal 
reception and rejection of heat and the vertical lines be and 
da show the reversible adiabatic changes. The corresponding 
corners of the cycle are for convenience lettered the same as in 
Fig. 18. 

(b) Since for reversible changes with ideal gases, 



AQ 



r 



the area abef under the isothermal expansion ab represents heat 
AQi received from the hot body, and the area cefd is similarly 
proportional to heat AQ2 rejected to the cold body during the 
isothermal compression cd. The difference abed is the area of 
the cycle and represents heat converted into work. Then 

AQi = Ti {^i—4>a) and AQ^ = T2 (<^c —<i>d) = T2 {4>h — 4>c) 
and 

Ff = ^Ql - ^Q^ = ri (0fe - ^a) - T2 (cj>, - Ct>a) 
^' AQy Ti (06 - 4>a) 

= 7^ — -J as before. 



GAS CYCLES 89 

53. Criterion of Maximum Efficiency. That an ideal engine 



may have the maximum possible efficiency, 



Ti 



Ti 



when 



ceiving heat from a body at temperature Ti and rejecting heat 
to a body at temperature T2, it is necessary that — 

(i) All heat received from the hot body be taken when the working 
substance has the same temperature as that body; and 

(2) All the heat rejected to the cold body be given it when the 
working material has the same temperature as that body. 

This is easily proved from 
the T0-diagram, Fig. 21. Im- 
agine heat to be received re- 
versibly along some such line 
as d' a' b, with the tempera- 
ture of the working substance 
varying from Td' to Ti. Obvi- 
ously less heat is received than 
if the reception had been iso- 
thermal, because the area fd' 
a'be ( = fabe — ad' a') is less 
than the area jabe. The work 
done is also less because the 
area dd'a'bcd ( = dabc — ad' a') 
is less than dabc. But since 
the area ad' a' is lost in both 







a 


a 


^,J , 


h 






s 

'^ 


rM 




1 






',}' y 






il 


]sullnilii;il '^--' 


\ 


















i 






t 


f 













Entropy 
Fig. 21.- 



T</)-Diagram of Carnot Cycle. 



cases, and since the (smaller) area representing work is affected 
more than the (larger) area representing heat received, it follows 
that 

a'bcdd' ^ abed 



< —r~. and Ef < Ef. 



a'bcefd' abef 

A similar proof would show that the rejection of heat along a 
line such as b'c' also gives a cycle which is less efficient than that 
with isothermal heat rejection.* 



* Confusion is sometimes caused by the apparent contradiction of these state- 
ments and those given as propositions (i) and (2) in Section 50. It should, how- 
ever be noted that a very distinct limitation is put upon the reversible engines 
considered in that section. They receive all their heat at temperature Ti from the 
hot body in reversible fashion and reject reversibly to a cold body at temperature 
T2. On the other hand, engines receiving heat along such a line as d'a', Fig. 21, 
could only do so reversibly by employing a string of hot bodies with temperatures 



90 



HEAT-POWER ENGINEERING 



54. The Constant- Volume Regenerative or Stirling Cycle, (a) 
In this cycle, which is drawn to PV-co6rdinates in Fig. 22, 
the gas receives heat from the hot body and 
rejects heat to the cold body along the iso- 
thermals ab and cd exactly as in the case of 
the Carnot engine. The two adiabatics of 
this latter case are, however, replaced by the 
two constant volume lines be and da. 

The line be is supposed to be obtained by 
allowing the working substance to reject heat 
to a body so arranged that it stores that heat 
in such a manner that (i) each part of the 
body is always at the same temperature as 
the contiguous gas, (2) the temperature of 
each part remains constant, and (3) each in- 
crement of heat after storing is maintained at 
the temperature of reception. The line da is 
supposed to be obtained by the return of the 
stored heat to the gas by a reversal of this 



a 








\ . 






\ 






\ 










d 


V 






°''W 


' 



Volumes 

Fig. 22. — PV-Dia 
gram of Constant-Vol 
ume Regenerative operation 
Cycle. Air as work- 
ing substance. Same 
pressure range as in 
Fig. 18. 



(b) Such a heat storing and restoring body 
is known as a Regenerator and in its perfect 
state is of course purely ideal. It may be ap- 
proximated, however, by a long pipe of heat- 
insulating material filled with wire gauze or equivalent, and with 
temperature Ti at one end and T2 at the other. As hot gas 
flows through in the direction T1T2 it will impart heat to the 
walls and filling at a progressively decreasing temperature and 
give the change be; while da may be obtained by causing gas to 
flow through the regenerator in the opposite direction. 



The Mechanism of the Stirling Engine. 

(c) The machinery necessary for the carrying out of such a 
cycle is shown in Fig. 23. The cylinders, Y and Fi, and the hot 
and cold bodies, U and X, are similar to those used in the Carnot 
engine. The tube R is the regenerator just described and its 

varying from T/ to Ta by infinitesimal elements, so that the gas might without 
sensible error be said to receive each element of heat when at the same temperature 
as the body supplying it. This is distinctly contrary to the assumptions of Section 
50 as reiterated above. 



GAS CYCLES 



91 



Yi 





R 


1 


LH^nJ-^^rr-rrrn^ 


i| 



\ 



Fig. 23. — Machinery of Constant- 
Volume Regenerative Cycle. 



contained volume is assumed to be negligible compared with 
that of either cylinder. 

Imagine the piston in Fi at the bottom of the cylinder and 
that in Y at the top, as the result of the expansion ab, Fig. 22. 
Y is then filled with a gas with conditions shown at b. Now 
drive the right piston down, thus 
forcing the gas through the regen- 
erator, and allow the left piston to 
rise at just the rate necessary to 
keep constant the total volume of 
the gas. During this process the 
regenerator will absorb heat and 
its temperature will grade from Th 
at the right to Tc at the left. 
When the piston in Y has reached 
the bottom of its stroke all the 
gas will be in Fi, the piston in the 
latter will be at the top of the stroke, and the constant-volume 
line be will have been produced. Now hold the right piston sta- 
tionary, bring the cold body up to cylinder Fi and force the pis- 
ton into this cylinder, until the volume occupied by the gas is 
that shown at d, in Fig. 22. This will produce the isothermal com- 
pression. Free the piston in F, continue the downward motion of 
that in Fi until it reaches the bottom of its cylinder, and simul- 
taneously allow the right piston to rise as much as is necessary to 
keep the volume constant. This will give the line da of the dia- 
gram, and the gas in passing through the regenerator will rise in 
temperature from Td ( = T^ to r„ ( = T^). Finally fix the left pis- 
ton in its position, bring the hot body up to cylinder F, and allow 
the gas to expand iso thermally from a toh, completing the cycle. 

Work Obtained per Unit Weight of Gas by Use of 
Constant-Volume Regenerative Cycle. 

(d) The work theoretically available from an engine using this 
cycle can be found, as in the case of the Carnot engine (see 
Section 49 (d), by summing up the quantities of work done 
during each process of the cycle. This is done in the following 
tabulation in which the letters in the first column refer to Fig. 
22. It is evident from the figure that, as before, the ratios of 
expansion and compression are equal. Thus, using unit weight, 



92 HEAT-POWER ENGINEERING 



Line. 


Process. 


Work Done 
/Ft.-Lbs.\ 
VLb.-Gas/ • 


ab 
be 
cd 
da 


Isothermal Expansion 
Isovolumic Change 
Isothermal Compression 
Isovolumic Change 


+ RTi log, r 

- RT2 log, r' 




Net work per cycle = RTi log, r — RT2 log, r', and since r = r' , 

= (T,- T2) Rloger ft.-lbs. . . . (73) 
Thus 

A£ = (^'-^;>/'°g'- B.t.u. . . . (74) 

Efficiency of the Constant-Volume Regenerative Engine. 

(e) With an ideal regenerator the isovolumic processes he and 
da would he ther mo dynamically reversihle, and the isothermal 
compression and expansion, as in the Carnot engine, are also 
reversible. The cycle as a whole must then he reversihle, and 
therefore its efficiency must equal the efficiency of the Carnot cycle.. 
This may be proved as follows : 

(f) With unit weight of gas, the heat received from the hot 

body may be called AQi, and as before it must equal ^~~s~* 

The heat rejected to the cold body is similarly AQ2 and is equal to> 

RT^loger' RTAoger . . . , 

— ^ — = T^ — ' smce r is equal to r . 

778 778 

The external work done, or the mechanical energy made 
available, must equal the difference between the work done by 
the gas during the isothermal expansion and the work done 
upon it during the isothermal compression, hence it must be 

778 AE = RTi log, r- RT2 log, r. 

Then the efficiency is 

^ AQi - A(22 ^ RT.log^r-Rnioger _ T, - T2 , . 
^ AQi RT.loger ~ T, ' ^^^^' 

There is often difficulty at first in realizing that this cycle, 
which has the same efficiency as the Carnot cycle, fulfills the 
criterion of maximum efficiency stated in Section 53. Careful 
study will show, however, that the statements in that section 
apply only to heat transfers between the working substance and 



GAS CYCLES 



93 



bodies external to the actual engine — i.e., the hot and cold 
bodies. The heat given up or received by the gas during the 
constant-volume changes, i.e., Cv(Ti— T2), is really stored and 
restored reversibly and does not enter or leave the system. 

T0-Diagram of Constant-Volume Regenerative Cycle. 

(g) Fig. 24 shows the T^-diagram of this cycle as abed super- 
imposed upon that of the Carnot cycle ahc'd'. For convenience 













a 






b 










.,o^^ 


1 


..,<>% 


y 


^ 






^ 


^ 




A 


p> 








d 






<^ 


i' 






-%' 








c 






i 





















































Entropy 
Fig. 24. — T0-Diagram of Constant-Volume Regenerative Cycle. 
Same temperature range as in Figs. 18 and 21. 

in comparison the two cycles are drawn for the same temperature 
range. 

The lines be and da are obtained from Eq. (63) and are evi- 
dently parallel curves. The areas bc'e and ad'd are, therefore, 
equal, hence abed must equal abe'd'. Each of these areas, how- 
ever, represents the heat converted into mechanical energy. The 
heat supplied in each case is shown by the area under ab. There- 
fore, the heat supplied in each cycle being the same, and the work 
done being the same, the efficiencies are equal. 



55. The Constant-Pressure Regenerative, or Ericsson, Cycle. 

The PV-diagram for this cycle, shown in Fig. 25, differs from 
the cycle last considered only in the fact that the regenerator proc- 
esses are carried on at constant pressure instead of at constant 



94 



HEAT-POWER ENGINEERING 



d ^ 


a 




i 






1 


\ 






V 




c 



















Volumes 

Fig. 25. — PV-Dia- 
gram of Constant Pres- 
sure Regenerative Cy- 
cle. Air as working 
substance. Same vol- 
ume range as in Fig. 
22. 



volume. The same mechanism may be used as in the last case^ 
and the cycle, being reversible, must have the same efficiency. 
The T(^-diagram of this cycle is similar to 
that of the constant-volume cycle shown in 
Fig. 24. The curves corresponding to he and 
da of that figure are obtained from Eq. (61) 
and of course have a different slope; other- 
wise nothing is altered, and statements con- 
cerning one of these cycles are, in general, 
true of both. 

56. The Constant-Volume Heat-Change^ 
Otto, or Beau de Rochas Cycle, (a) This 
cycle, the PV-diagram of. which is shown in 
Fig. 26, consists of 
two adiabatics he and 
da and two constant 
volume lines ah and 
cd. Heat is received 
from the hot body 
along the line ah, the 
pressure and temper- 
ature rising while the 
volume remains con- 
stant. Heat is rejected to the cold 
body along the line cd, the pressure and 
temperature dropping while the volume § 
remains constant. 

(b) The reception of heat is irreversi- 
hie, since the temperature of the hot 
body is at least as high as that which 
the gas attains when reaching condition 
h, and therefore must be higher than 
that of the gas during the entire recep- 
tion of heat AQi. The same is true for 
the rejection of heat along cd, the cold body having a tempera- 
ture at least as low as that of the gas at d. This case is the 
first one cited in Section 35 as a process intrinsically irreversible. 
This cycle is not only irreversible, but, as is evident, it does 
not fulfill the criterion for maximum efficiency (Section 53), and 



b 


























V 






a 


\S 


I 






\ 


>1 








d 





Volumes 

Fig. 26. — PV-Diagram of 
Otto Cycle. Air as working 
substance. Conditions at h 
same as those at a in Fig. 18 
and lowest pressure same as 
in that case. 



GAS CYCLES 



95 



hence has an efficiency lower than that of the cycles previously 
described. It is, however, the only one of the four gas cycles 
so far considered which is of any great practical importance. 



Mechanical Energy Obtained per Unit Weight of Gas 
Operating in Otto Cycle. 

(c) The following tabulation gives the mechanical energy 
changes for each line per unit weight of gas: 



Line. 


Type of Change. 


Work in Ft.-lbs. Done by 
Gas. 


ab 


Constant- Volume Pressure Rise 


O 


be 


Adiabatic Expansion 


R{n-Tc) 

7-1 


cd 


Constant- Volume Pressure Drop 


O 


da 


Adiabatic Compression 


R{Ta- Td) 
7-1 



The summation of the last column gives the net work per cycle 
per unit weight of gas, as « 



Net work 



FromEq. (33), 



R 



(n- Tc- Ta+ Td) ft.-lbs. 



is equal to K^, giving 



(76) 



7-1 
Network = 778 AE = K^Tb - Te - T^ -\- Td). . (77) 

(d) This same result could have been obtained more briefly as 
follows : The mechanical energy obtained must equal AQi — AQ2, 
when measured in heat units; that is, AE = AQi — AQi- Since 
the heat changes take place at constant volume, AQi = C„ 
in - Ta) and AQ2 = C, (Tc - Td), 
hence, in ft. lb. units, 

778 AE= KATb- Ta) - K, (T, - Td) 

= K^n- Ta-Tc+ Td) 

which is the same as Eq. (77). 



(e) Writing 



96 HEAT-POWER ENGINEERING 

Efficiency of Otto Cycle. 

AE ^ AQ1-AQ2 
^' AQi A(2i 

and substituting in the last form gives 

£^ ^ CAn- Ta)-CATc- Ta) 

Cv{Tb — Ta) 



r. - T. 



^ rj. ^ (78) 

This expression can be further transformed and simplified 
so that important conclusions can be easily deduced. Since the 
curves he and da are adiabatics, Eq. (51) gives 

n /FfcV-^ , Ta (VaV-^ 

Tr\vj ^^^ TrwJ 

Since Va = Vb and Vc = Vd 



(r'=(r' 



and therefore 
















- 


To 


Ta 

Ta 


and 


To- 

n- 


Ta 

Ta 


Ta 

Ta 


Substituting from this in 


(78) 


gives 










Ef.= 


= 1 - 


Ta 


_ n 


- Ta 

Ta 





(79) 



(80) 



and Ef. = 1 -(^^J ' (81) 

Thus it is evident — 

(i) That the efficiency of this cycle is independent of the upper 
temperature, but depends only upon the temperature range of 
adiabatic compression. 

(2) That with the same value of Pa, the less the volume of 
one pound of gas at the end of compression the higher the efficiency. 

(3) That with the same temperature Ta, the higher the tem- 
perature at the end of compression the higher the efficiency. 

Eq. (81) shows that the efficiency of the cycle may vary with 
different real gaseous working substances because the value of 7, 
as shown in Table I, is not the same for different gases. This 
is in marked contrast to the cycles previously considered, where 
the efficiency could be expressed entirely in terms of the tem- 



GAS CYCLES 



97 



peratures of the hot and cold bodies, and where the efficiency 
was independent of the individual characteristics of the gaseous 
working substances. 

Writing the Carnot efficiency 





T,- 


T2 




T, 




and the Otto efficiency 


Ti 






T, 




Ta- 

Ta 


I^ = 


1 - 


' Ta' 


= 1- 





■■ I ~ holds for 



inspection shows that for the same upper and lower tempera- 
tures the Otto efficiency must be the smaller, as Ta must be less 
than Ti, 

T(/)-Diagram of Otto Cycle. 

(f) In reality the T^-diagram of this cycle cannot be drawn 
in any such direct manner as was used in the preceding cases. 

The reason for this is that the equation A</) 

reversible processes only, 
whereas two processes in 
this cycle are irreversible 
(see (b)). 

It is possible, however, to 
draw a T^-diagram for this 
case by making use of the 
fact that the entropy change 
accompanying an alteration 
from one PVT condition to 
another must always he the 
same, no matter how the 
change from the first state to 
the second occurs. 

To find the entropy 
changes occurring as the gas 
receives heat along the line 
ah in Fig. I"], it is then only 
necessary to discover some 
reversihle method of supplying that heat in such a way that the 
conditions of the gas at every individual point on ah will be the 
same as when the heat supply is irreversible. 




T</)-Diagram of Otto Cycle. 
Air as working substance. Same tempera- 
ture range as that in Figs. 18 and 21. 



98 



HEAT-POWER ENGINEERING 



Such a heating process would result from the use of a series 
of reservoirs with temperatures graded from Ta to Tb. The gas 
can then receive each increment of heat from a reservoir having 
the same temperature as it possesses at the instant, and there- 
fore the gas can thus be heated reversibly. 

The total entropy change would then be 



A0 



= C„ loge Y 



and by the use of this equation the T0-diagram can be drawn as 
in Fig. 27. The diagram in this figure shows the same changes 
as are represented by PV-coordinates in Fig. 26. The dotted 
rectangle is the Carnot cycle originally given in Fig. 21. 



57. The Constant-Pressure Heat-Addition, Bray ton, or Joule 
Cycle, (a) This cycle, like the last, is an irreversible one in the 
thermodynamic sense, but it is impor- 
tant because of its practical application 
to. certain purposes which will be con- 
sidered later. It is now necessary to 
derive the type equations for the cycle, 
as has been done in the preceding cases. 
Fig. 28 shows the Joule cycle drawn 
to PV-co6rdinates. Starting at a, heat 
is added to the working substance by 
the hot body, volumes and temperature 
increasing at constant pressure, until the 
point h is reached. Obviously the tem- 
perature Ti, of the hot body, must be 
at least as high as that of the gas at h, 
and therefore higher than that of the 
gas at a. The heat addition is there- 
fore irreversible. 

From h the gas expands adiabatically 
to c, then rejects heat irreversibly, main- 
taining constant pressure until the vol- 
ume Vd is reached, and is then compressed adiabatically to o, 
completing the cycle. 



a 


h 








\ 








\ 


V 






' 




r 










V \ 








V 


V 


c 


d^ 













Volumes 

Fig. 28. — PV-Diagram of 
Joule Cycle. Air as working 
substance. Adiabatic expan- 
sion with same pressure range 
as in Fig. 26. 



GAS CYCLES 



99 



Mechanical Energy Obtained per Unit Weight of Gas 
Operating in Joule Cycle. 

(b) As before, the useful effect per unit weight of gas can be 
found by tabulation. Thus: 



Type. 



Constant-Pressure Expansion 
Adiabatic Expansion 
Constant-Pressure Compression 
Adiabatic Compression 



Mechanical Energy (Ft. -lbs.) 
Made Available. 



+ Pa {Vb 


-Va) 


. PbVb- 


PcVc 


' 7- 


1 


- Pc (Vc 


-Vd) 


PaVa- 


PdVd 



The summation of the last column gives for the cycle 



Net Work = Pa (V5 - V^) + 



7- 1 



P V — PjVj 

Pc (Ve - Vd) - ^-^^ ^ ft.-lbs. (82) 



(c) This expression could be simplified, but it is hardly worth 
while, as a shorter one can be obtained more easily in the follow- 
ing manner. 

Writing available mechanical energy, or work done, as 

AE = {AQi - AQ2) B.t.u., 
it follows from the character of the lines ab and cd that 

AE = CATb- Ta)-CATc- Ta) 

= Cp(n- r„- r,+ r,) B.t.u. . . (83) 



and 



778 AE = KAn- Ta) -KATc- Ta) 

= Kj>{Tb- Ta- To+ Ta) ft.-lbs. 



(84) 



HEAT-POWER ENGINEERING 



(d) Since 

Ef.= 
it must be in this case, 



Efficiency of Joule Cycle. 

AQi - AQ2 



Ef. 



AQi 
To) -C^Tc- Td) 



Cp {Tb 

n - r, . 

n- Ta 



To) 



This can be further simplified by using Eq. (52). 

then, since 

Pa = Pb and Pd = Pc 

T^^Td^ Tc - Td 

Tb Ta Tb-Ta 

Substituting this in Eq. (85) gives 

Ef. = l-'^, . . . 



• . (85) 
From this 




(86) 



a result similar to that obtained for the 
Otto cycle. 

The last equation can, by simple sub- 
stitution, also be written 



Ef. 



r^r^' 



(87) 



which is likewise similar to the corre- 
sponding form for the Otto cycle". 

T0-Diagram of Joule Cycle. 

(e) By replacing the irreversible iso- 
barics by equivalent reversible proces- 
voiumes ggg^ ^]^g T^-diagram to represent this 

Fig. 29.— PV-Diagram of ^y^\^ ^^^ be constructed, as was done 
'^^Tl?r\.'^\-17TyZl for the Otto cycle; but as this diagram 
is of little practical value it will be 
omitted. 



rsubstance. The lines he and 
'Cd coincide with the lines sim 
ilarly lettered in Fig. 26. 



58. The Diesel Cycle, (a) This cycle, drawn to PV-coordi- 
nates, is shown in Fig. 29. The heat is added from the hot body 



GAS CYCLES 



lOI 



during the constant-pressure expansion ab, and then the gas ex- 
pands adiabatically from b to c. Heat is discharged to the cold 
body while the pressure of the working substance decreases from 
c to d at constant volume. The cycle is closed by the adiabatic 
compression da. The Diesel cycle is irreversible for the same 
reasons that the Otto and Joule cycles are. 

Mechanical Energy Obtained per Unit Weight of Gas 
Operating in Diesel Cycle. 

(b) As before, the amount of mechanical energy made avail- 
able can be found by tabulating: 



Line. 


Character. 


Work (Ft. -Lbs.) Done by 
Unit Weight Gas. 


ab 
be 
cd 
da 


Constant-Pressure Expansion 
Adiabatic Expansion 
Constant- Volume Pressure Drop 
Adiabatic Compression 


+ Pa (Vfe - V„) 

PbVb - PcYc 

• 7 - 1 

PaVa - PdVd 

y - 1 



The summation of the last column gives for the cycle 
Net Work = 778 AE = Pa (Yb - V„) + FJll^zIili 



PaVa - PdYd 



ft.-lbs. 



(88) 



(c) This expression need not be simplified, since, as in previous 
cases, there is a more convenient way of finding a short ex- 
pression for the work done. Writing 

AE = (A(2i - AQ2) B.t.u., 

it follows that, in the case of the Diesel cycle, 

AE= Cj,{Tb- To)- C,{Tc-T,) B.t.u. . . (89) 



and 



778 A£= Xp(n- r„) -x,(n- r,) ft.-lbs. . (90) 



HEAT-POWER ENGINEERING 



(d) Writing 



Efficiency of Diesel Cycle. 



Ef.= 



AQi - A(22 
A(2i 



Ef. 



the efficiency in this case must be 

CAn- Ta)-CATc-Ta) 

" ' LCp n - rj Lt n - rj ^^ ; 

This has the same form as Eq. (85), for the efficiency of 
the Joule cycle, with the exception of the introduction of 1/7. 
It should, however, be noted that the temperature term is not 
numerically the same in both cases, on account of the difference 
in the shape of the two cycles. 

(e) By substituting reversible processes for the irreversible 
ones, a T^-diagram equivalent to this cycle can be constructed. 



GAS CYCLES — TABLE III 



CYCLE 


WORK-FT.LBS. 
PER LB. OF GAS. 






NAME 


PV-DIAGRAM 




GENERAL 


Any Number 
W> of Processes 
^-^ Enclosing 


= Area Enclosed (A) 
<=AQ,xEfr.x778. 
=778 AE 
=778(AQi-AQ2) 


=Ilesult-=- Effort 
= (AQ-AQ2)-^/\Qi 




CARNOT 


_ Isotliermals 
\} and 
-j^ Adiabatics 


= CT-TORloger 


= ^=i-(^ 




STIRLING 


vT Isothermals 
%f, and 
TgN Isovolumics 


( 1 


(< 




ERICSSON 


-p Isothermals 
T5 Isobarics 


1 1 


< ( 




OTTO 


^ Adiabatics 
^fl Isovolumics 


= K„(T,-T-VTJ 


-^-^MV' 




BRAYTON 

OR 

JOULE 


ab Adiabafics 


=Kp(T,-T-T,+T,) 


Cl 




DIESEL 


ah Adiabatics 

^^ c Isobaric and 

d Isovolumic 


=K/VT„)-K„(T,-T^) 


=1 VJ'^-^ 











CHAPTER IX. 

VAPORS. 

59. Vapors and Gases. When materials change from the 
liquid* to the gaseous state they do not immediately reach the 
condition in which their behavior even approximately obeys the 
laws of ideal gases. It is customary to designate materials as 
Vapors when in this intermediate condition. It will appear 
later that when strictly interpreted the term vapor will apply to 
many of the materials with which the engineer deals and which 
he is accustomed to call gases. 

60. Formation of Vapor, (a) When a liquid is heated under 
constant pressure its temperature will first rise until it reaches a 
certain temperature which is dependent upon the pressure under 
which it exists; after which further addition of heat will cause 
some of the material to change physical state at constant tem- 
perature, this temperature being the one fixed by the pressure 
existing. The amount of material that has changed state will 
increase as this further addition of heat progresses, and if sufficient 
heat is added all the liquid present will thus change its state. 
The material formed during this change of state is called a vapor. 

(b) Considering the process for the first time, one would 
recognize two possible methods of formation of vapors, and 
without previous knowledge would not be able to decide be- 
tween them. Thus: 

(i) The liquid as a whole might gradually change from liquid 
to vapor, all of it being at any one time in exactly the same con- 
dition of transformation. Or, 

(2) Parts of the liquid might progressively change to vapor as 
the necessary heat became available, leaving the remainder still 
in the form of liquid. 

Usually vaporization occurs by method (2), and as heat is 
added more and more vapor appears at the expense of liquid. 

* Or directly from the solid, as in " sublimation." 
103 



I04 



HEAT-POWER ENGINEERING 




Thus when one-fourth of the total heat necessary for complete 
vaporization is added one-fourth of the liquid will be vaporized, 
and so on until vaporization is complete. 

(c) In the sections which follow the generation of vapor may 
be conveniently studied by imagining the process carried out in 
the device illustrated in Fig. 30. It 
consists of a vertical cylinder with 
closed end down, containing a friction- 
less piston of given weight, — all being 
placed under a bell jar in which a per- 
fect vacuum is maintained. 

Assume now that one pound of liq- 
uid is inclosed in the cylinder beneath 
the piston. The total pressure on the 
upper surface of this liquid will be 
that due to the weight of the piston, 
and since it is evenly distributed over 
the entire surface it may be desig- 
nated as P pounds per square foot of 
surface. 

Any liquid may be used and, in general, may have any tem- 
perature between that of solidification and that of vaporization 
at the chosen pressure. It is, however, customary to assume the 
temperature at a convenient value dependent on the physical 
characteristics of the liquid dealt with. 

In the case of water, and of all other liquids for which such a 
temperature is at all convenient, the engineer is accustomed to 
refer all vaporization phenomena to a datum temperature of 
32° F. As this is the melting temperature of ice under ordi- 
nary conditions, it is readily checked and is hence a very satis- 
factory standard. 

To make the results of the process under consideration con- 
form to the engineering reality, the liquid beneath the piston, 
in Fig. 30, will be assumed at 32° F. 



Fig. 30. 



61. Heat of the Liquid, (a) If heat is added to the liquid 
beneath the piston in Fig. 30, the temperature will rise and, in 
the case of water, at the approximate rate of i° F, for each B.t.u., 
since the specific heat of water at constant pressure is approxi- 
mately I. In any case the rise will take place at the rate of 



VAPORS 105 

1° F. for each addition of heat equal to Cp, the constant-pressure 
specific heat of the Hquid dealt with. This will continue until a 
temperature is reached at which vaporization begins. This tem- 
perature will depend upon the value of the pressure, and in 
any case has to be determined by experiment. Thus with 
water at atmospheric pressure (equal to 14.7 pounds per square 
inch, or 14.7 X 144 = 21 16.8 pounds per square foot), the tem- 
perature will be 212° F. ; while for a pressure of 100 pounds per 
square inch (equal to 100 X 144 = 14,400 pounds per square 
foot) the temperature will be about 327° F. These various tem- 
peratures are called the Temperatures of Vaporization and will 
be designated by the symbols /„ and T^ respectively for Fahr. 
and Absolute temperatures. When it is necessary to indicate a 
particular temperature, the corresponding pressure in pounds 
per square inch will follow the subscript v; thus, the tempera- 
ture Fahr. of vaporization at atmospheric pressure would be 
ivu-7 or temperature absolute T^h.t. 

(b) The heat added during the process of raising the tempera- 
ture from 32°, or other datum level, to the temperature of vapor- 
ization is called the Heat of the Liquid and is designated by g. 
Obviously it has a different value for every different pressure 
and it is customary to tabulate these values with others in so- 
called Vapor Tables. In general 



/ 



CpdT, (92) 

the integration being performed between the datum tempera- 
ture as the lower limit and the temperature corresponding to the 
pressure in question as the upper limit. 

If the specific heat of water were exactly equal to unity at all 
temperatures, the value of q for this material for any temperature 
or pressure of vaporization could be found from the equation 

q = tv-32; (93) 

and since these values vary but slightly from those determined 
by experiment, this equation is often used by engineers. For 
accurate work the experimentally determined values given in the 
steam tables should be used. 

(c) Eq. (93) could not be used, even as an approximation, 
with any liquid other than water, since it depends upon the 
assumption that the specific heat of the liquid is invariably 



lo6 HEAT-POWER ENGINEERING 

equal to unity. If, as before, the specific heats of liquids at con- 
stant pressure are designated by Cp, and if they are assumed con- 
stant over the ranges of temperature considered, the equation 

g = Cp (/. - 32) (94) 

may be used in determining the heat of the liquid for any tem- 
perature or pressure of vaporization. Note that there are liquids 
which vaporize at ordinary pressures below the temperature of 
32° F. In such cases a datum temperature lower than 32° may 
be taken from which the heat of the liquid is calculated. This 
necessitates a different form of equation. In its most general 
expression this would become 

a = CAT.- To), (95) 

where 7*0 stands for any arbitrarily chosen datum. 

62. Latent Heat of Vaporization, (a) Consider now the pound 
of liquid which has been raised to the temperature t^. With 
further addition of heat vaporization occurs. The marked char- 
acteristics of vaporization under the assumed conditions are (i) 
the very great increase of volume at constant temperature and 
pressure, (2) the change of the physical state of the material from 
liquid to vapor, and (3) the enormous quantity of heat absorbed. 

(b) The process carried out in the apparatus of Fig. 30 would 
result in driving up the piston to some higher position in the 
cylinder, against the pressure exerted by that piston on the upper 
surface of the vapor. Evidently, here, force would act through 
distance and therefore external work would be done. This 
work could not be done without a supply of energy, and, since 
heat energy is the only form supplied during the process, it 
follows that at least some of this heat must have been used for 
the doing of the external work. Let F be used to designate the 
area of the piston face in square feet, and L the number of feet 
the piston is moved during the vaporization of the entire pound 
of liquid under consideration. 

Then the foot-pounds of external work done per unit weight 
are 

778 ^E = {PF) L, 

which, rearranged, becomes 

778 AE = P (FL) = P (V2 - Fi), . . . (96) 



VAPORS 



107 



where Vi represents the volume occupied by the liquid and V2 
that occupied by the vapor. It is customary to designate the 
increase of volume (V2 - Vi) by the letter u, hence the external 
work done, in foot-pounds, is 

778AE = Pu, (96a) 

and its value in thermal units can be found by dividing Pu by 

778. Representing --^ by ^, the expression for the B.t.u. of heat 

778 

used in the doing of external work becomes 

AE = APu (97) 

This quantity is called the External Latent Heat of Vaporiza- 
tion. It has a different value for every different pressure at 
which vaporization takes place, and these values are tabulated 
in the Vapor Tables already mentioned. 

It is very necessary to observe that the term external "latent 
heat" is a misnomer. The heat used for the doing of external 
work does not exist as heat energy in the vapor, for, during the 
process of vaporization, it is changed into mechanical energy 
which is extraneous to the vapor itself. The case is somewhat 
similar to isothermal expansion of a gas. This heat is con- 
verted into mechanical energy as rapidly as received. Hence, in 
a piston engine, the external latent heat may be considered as 
external work delivered by the piston rod. If the energy after 
reception can be said to be " latent," it must be latent mechani- 
cal energy and not latent heat energy. It is stored, if stored at 
all, in the piston or other similar part of the apparatus, and is 
in no sense in the vapor. 

(c) Experiment shows that the heat used during the process 
of vaporization is not all accounted for by the external latent 
heat. Inspection of Eq. (i), 

A(2 = A5 + A/ + AE, 

suggests the reason. In this case AQ represents the heat added 
to vaporize the liquid. As the temperature does not change 
during vaporization, no heat can be used as sensible heat, hence 
A^ = o; but some of it may be used for the doing of internal 
work, A/. In fact the striking change of properties during this 
process could not occur without a very great readjustment 
within the material. The part of AQ which does not become 



I08 HEAT-POWER ENGINEERING 

external latent heat is supposed to be used for doing this internal 
work, and is therefore called the Internal Latent Heat. It is 
designated by the symbol p and is tabulated in the Vapor Tables. 

Recent work has led to the conclusion that liquid water is a 
more complex material than was originally supposed. It seems 
probable that instead of being simply a collection of molecules 
with formula H2O it is really a mixture of at least three different 
kinds of molecules, H2O, (H20)2 and (H20)3. It also seems prob- 
able that during the formation of vapor some of the more com- 
plex molecules break up into simpler form. If this is so, a 
possible use of at least part of the Internal Latent Heat in the 
case of water becomes evident since it would be used for break- 
ing up the complex molecules. " Internal " latent heat would 
then be a correct name to apply to this part of the heat as it 
is latent within the substance, though there is room for argu- 
ment as to whether it is latent as heat. 

(d) The sum of the two latent heats, p and APu, is called the 
Total Latent Heat of Vaporization, and is designated in the 
tables by r. Thus ^ = p + APu 

63. Total Heat per Pound of Vapor, (a) Using symbols, the 
total heat, above the arbitrarily chosen datum temperature, per 
pound of vapor at any pressure P, is the sum of the sensible 
heat, the internal latent heat, and the external latent heat; thus 
it is 

g.p + Pp + {APu)p^ g_^ + rp, . .-. . (98) 

and calling this X gives 

Xp = & + rp, . . . . . . (99) 

which is also given in the tables. 

(b) Had the addition of heat in the process under considera- 
tion ceased before the entire pound of liquid had been vapor- 
ized, the cylinder would have contained both vapor and liquid 
at the same temperature. Representing by y the fraction of the 
total pound vaporized, the " heat of the vapor " * present must 
be 

A(2' - yqj> + ypp + y {APu)p 

* The expression " heat of " will hereafter be used to designate the quantity- 
necessary to bring the material in question to the condition under consideration, 
either from liquid at datum temperature or from liquid at the temperature of 
vaporization. The context will indicate which is referred to in any case. 



VAPORS 109 

and that of the remaining liquid must be 

hence the total heat of the material in the cylinder is 
AQy, = AQ' + AQ" 

= qp + yPp + yiAPti)p .... (ioo> 
= 2p + yfp (looa)' 

which will be equal to Eq. (98) when 3^ = 1, that is, when the 

entire pound has been vaporized. 

64. Saturated Vapor, (a) The process assumed in the pre- 
vious sections is really more or less idealized. In real cases, 
such as that taking place in the steam boiler, the vaporization 
does not progress so quiescently that the vapor separates en- 
tirely from the liquid and collects above it in the simple fashion 
already described. Instead, the formation of vapor is gen- 
erally more or less violent, and, in separating from the body of 
the liquid, the vapor carries with it small drops of that liquid 
still unvaporized but mechanically entrained. These may often 
be carried great distances by a stream of vapor, and their sepa- 
ration from that vapor frequently presents considerable diffi- 
culty. 

(b) Such mixtures of vapors and liquids are called Wet Vapors ^ 
to indicate the presence of the liquid; and when the entrained 
moisture has been entirely eliminated the material is called Dry 
Vapor. Since, under the conditions assumed in connection with 
Fig. 30, the liquid must all be raised to the temperature of 
vaporization before any of it can be converted into vapor at the 
same temperature, it follows that the vapor and liquid in such a 
wet mixture are in thermal equilibrium; that is, if there is any 
tendency for heat transfer from liquid to vapor, there is an equal 
tendency towards transfer in the opposite direction. With no 
heat lost to surrounding materials, such a mixture would main- 
tain a constant composition indefinitely. 

Vapor when in thermal equilibrium with its liquid is called 
Saturated Vapor. It is termed Wet Saturated Vapor, or simply 
Wet Vapor, if containing entrained liquid and Dry and Saturated 
Vapor, or simply Dry Saturated Vapor, if free from moisture in 
suspension. 



no HEAT-POWER ENGINEERING. 

(c) At different pressures the quantity of heat necessary to 
maintain material in the condition of dry saturated vapor has 
different values, being greater the higher the pressure. Abstrac- 
tion of heat without change of pressure (and therefore without 
change of temperature) will cause partial or total condensation, 
but any vapor remaining will still be saturated vapor exactly 
like that which existed before condensation occurred. There- 
fore saturated vapor may be described as vapor so near the 
point of liquefaction that the removal of the slightest quantity 
of heat will produce partial condensation. Or (see following 
paragraphs) it may be described as vapor in which the maximum 
number of molecules, consistent with the maintenance of a vapo- 
rous state at the given pressure, exist in a given space. 

65. Quality, (a) Practically all saturated vapors in actual 
use contain some entrained moisture, and it is often necessary to 
express just how much of each pound of such a mixture is liquid 
and how much is vapor. This is done by using the fraction 
representing the proportion of mixture which is really saturated 
vapor. This fraction is denoted by x, and is called the Quality 
Factor, or Quality of the vapor or mixture. 

Thus if X is f, or 75 per cent, it means that three-quarters of 
every pound of mixture is vapor and the other quarter is liquid. 
The quality of the mixture would then be said to be 75 per cent. 

(b) The heat content above datum temperature of such a 
mixture could obviously be found by putting x in place of y in 
Eq. (100), since, so far as associated heat is concerned, it makes 
no difference whether the vapor and liquid are separated or 
intimately mixed. For wet vapor of quality x, the total heat 
above datum temperature is then 

A(2xp ^ qp + xpp -\- X (APu)p = qp-\- xrp. . (loi) 

66. Superheated Vapor, (a) Having converted an entire 
pound of liquid into dry and saturated vapor in the apparatus 
of Fig. 30, its condition may be further modified if the addition 
of heat is still continued. Experiment shows that this further 
addition causes the temperature of the vapor to rise above that 
which existed during vaporization. This process is known as 
superheating, that is, raising above the saturation temperature 
corresponding to the existing pressure. The material formed is 



VAPORS III 

called Superheated Vapor, and it becomes more and more like 
an ideal gas as its temperature is raised at constant pressure. 
Thus it increases in volume with the addition of heat, and a given 
space must hold fewer and fewer molecules as the rise of temper- 
ature continues. 

(b) To make the meaning of the term " saturated " clearer, 
imagine a superheated vapor to be cooled, at constant pressure, 
by the removal of heat. As temperature decreases the vol- 
ume also becomes less, and any given space holds more and 
more molecules until the temperature of vaporization is reached, 
at which point the material is reduced to the saturated condi- 
tion. There is then, in a given space, the maximum number of 
molecules which can exist as vapor under the conditions obtain- 
ing; and further removal of heat would allow some of these to 
collect and form molecules of liquid, — that is, it would cause 
partial condensation. The material remaining uncondensed 
would still be saturated vapor, and with further removal of heat 
more and more of it would condense until finally all would be- 
come liquid, if the removal of heat were continued sufficiently far. 

67. Heat per Pound of Superheated Vapor. The amount of 
heat added during superheating at constant pressure, to any 
temperature Ts, as described above, depends upon two things, — 
on the degree of superheat, which will be called D and equals 
{Ta — T-o), and on the specific heat Cp of the vapor. Then the 
heat added during superheating would be given by the following 
equation if Cp happened to be a constant: 

^QD = CpD (102) 

The total heat (above datum temperature) of one pound of 
superheated * vapor would be 

AQs= qp + Pp + {APu)p + CpD . . . (103) 

' ^ qp + rp -\- CpD = Xp + CpD. . . (103a) 

* Recent experiment has shown that liquid water can exist for a considerable 
length of time within a mass of superheated steam, despite the fact that the two 
are not in thermal equihbrium. This fact must sometimes be taken into account 
in dealing with superheated steam in practical problems, when sufficient time does 
not elapse to establish thermal equilibrium. The heat per pound of such a mixture 
would be _ 

Qxs = ?p + xrp + xCpD. 



112 HEAT-POWER ENGINEERING 

68. Diagram of Heat Changes during Vaporization, (a) The 

heat changes associated with the process of vaporization can all 
be graphically represented, as in Fig. 31, by plotting temperature 
as ordinates and heat added as abscissas. The figure is for 
water, but a similar diagram could be drawn for any material 
whose physical constants are sufficiently well known. 



boo 














r 




<r 






Xt50-- 




-— 1^ 




T' 


^■7 




150 Lbs. 


Sq. In. 


1 


!3 


. 


/ 




70 ." 


,„ 




I 


«o 






30 " 


" 


1 


1 


""/I 






10 ." 

Xixr— 


------ 


c 
— -^ 




a 


fi 














\ 


2 


)0 4 


6 


8( 


1000 1200 U( 



Heat.Added- B.T.U. 



Fig. 31. — TQ-Diagram for Vapor Phenomena. 



The line abed shows the relation of temperature to heat added 
while one pound of water under 10 pounds pressure is first 
heated from 32° F. to vaporization temperature (line ab) , is then 
completely vaporized (line be), and finally is superheated through 
a limited range (line cd). The lines abiCidi, ab2C2d^, etc., show 
the same things for the other pressures indicated. 

(b) A diagram drawn to a sufficiently large scale would show 
the line abbs, and lines cd, Cidi, etc., as slightly curved because of 
the variation in the value of the specific heat of liquid water and 
of the specific heat, Cp, of superheated water vapor. In draw- 
ing Fig. 31 an average specific heat was used for the liquid and 
an average over each temperature range cd, c^di, etc., for the 
superheated vapor. The latter accounts for the slight differ- 
ences in slope of the superheating lines. 

(c) The diagram shows how great an amount of heat is 
absorbed during the process of vaporization as compared with 
that used in bringing the liquid to the temperature of vaporiza- 
tion, or with that used in superheating. This is of great im- 
portance in heat engineering and will be fully considered later. 

Two other facts of importance are made evident by the dia- 



VAPORS 113 

gram: One is the small change of total heat, X, for a wide 
pressure range, as is seen by comparing the abscissas of c, Ci, 
etc.; and the other is the decrease of the total latent heat of 
vaporization, r, as the pressure rises. 

(d) This figure also shows the temperature changes and heat 
given up when superheated vapor at any of the given pressures 
is cooled to the saturated condition, then is condensed, and the 
resulting liquid cooled to 32° F. The engineer must often con- 
sider changes in this direction. 

69. Vapor Tables. Since the various values of g, p, APu, r, 
and \ are very frequently used by engineers and scientists, they 
are recorded, as already intimated, in the so-called Vapor 
Tables. There is of course a table for each material dealt with, 
so that it is customary to speak of " Steam Tables," " Ammonia 
Tables," " Carbon Dioxide Tables," etc. 

The various values of each quantity are usually tabulated in 
vertical columns, the first two columns giving pressures and 
corresponding temperatures of vaporization, and the succeeding 
columns giving the corresponding values of the various heat 
quantities. Certain other columns are usually added containing 
such values as the volume occupied by a pound of liquid and by 
a pound of dry and saturated vapor. See tables in Appendix. 

70. Saturation Curve, (a) Experiment shows that just as 
the saturated vapor of a given material at any particular tem- 
perature always exerts the same definite pressure, so also does 
one pound of dry saturated vapor at any temperature always 
occupy a definite volume. This latter is called the Specific 
Volume and is tabulated in the vapor tables. If the specific 
volumes are plotted against the corresponding pressures, the 
locus of the points is a PV-diagram similar to Fig. 32, which 
like the last is drawn for water vapor. 

(b) This curve, called the Saturation Curve, may be very useful. 
If one pound of material at a given pressure has a volume rep- 
resented by a point which falls to the left of the saturation 
curve, the material must be wet vapor; but if the point falls to 
the right of that curve, the material must be superheated vapor. 

In the case of most engineering materials, the volume occupied 
by one pound of liquid is negligible as compared with that of 
one pound of vapor. In the case of water, the volume increases 



114 



HEAT-POWER ENGINEERING 



nearly 1700 times when changing from liquid to dry saturated 
vapor under atmospheric pressure. If the volume of the liquid 
present be neglected, steam of 50 per cent quality would occupy 
0.5 the volume it would if dry and saturated, and steam of 75 per 
cent quality would have 0.75 of the volume of dry saturated 
steam, and so on. 

It follows that, if one pound of mixture is found to occupy a 
volume ab, Fig. 32, at the pressure indicated, it must have a 

















\ 










a 


-i-^ 


\ 








Wet 


Region 




^V. 
















~~ 



Specific Volumes 
Fig. 32. — Saturation Curve for Water Vapor. 

quality of x = — , if the volume of the water present is neglected. 

The case of superheated steam will be considered later, after the 
discussion of the experimental results. 

The area to the left of the saturation curve might be called 
the region of wet saturated vapor; and the area to the right, the 
region of superheated vapor. The curve itself would then repre- 
sent the boundary between the two, thus emphasizing the fact 
that dry saturated vapor is a unique condition at each pressure. 

(c) Because of the resemblance of the saturation curve to 
an expansion curve there is a tendency to regard it as represent- 
ing a possible expansion of vapor, that is, as an increase of 
volume during which the vapor remains dry and saturated 
throughout the entire process. Such an expansion might be 
obtained under very forced conditions, but normally no such 
process could be made to occur. It is then best to regard this 



VAPORS 115 

curve only as a boundary line between two fields and not as the 
graph of a process. 

71. Defining Conditions for Saturated Vapors. In dealing 
with ideal gases the variables to be considered are pressure, 
temperature, and volume. They are so interrelated that fixing 
any two determines the third. 

In the case of dry saturated vapors, however, the pressure, 
temperature, and volume are so related that the fixing of one 
determines the other two. This is not true of wet saturated 
vapors nor of superheated vapors. 

In the case of wet saturated vapors, the fixing of temperature 
determines the pressure, and vice versa, but the quality must be 
known in order to determine the volume occupied. 

Superheated vapors are more or less like gases, and in general 
the fixing of any two of the variables determines the third. 

72. Evaporation, (a) There is sometimes difficulty in harmo- 
nizing the phenomena of vaporization, just described, with what 
is commonly known as evaporation. There is no real difference 
in the phenomena, vaporization as so far considered being only a 
limiting case of evaporation. 

(b) In what follows it will be of material assistance if it is 
remembered that the so-called temperature of vaporization at 
any pressure is really the temperature of saturated vapor (wet 
or dry) at that pressure. 

Thus the pressure exerted by a saturated vapor is determined 
by the temperature of the space the vapor occupies, and the 
pressure corresponding to any temperature can be found in the 
vapor table for the material. 

(c) Experiment shows that when the surface of a liquid is ex- 
posed to a space which is not already filled with the saturated vapor 
of that liquid, vapor is generated until the space is filled with such 
saturated vapor, unless the liquid present is insufficient in amount. 
Of course vaporization ceases if the liquid is exhausted. 

If the condition of equilibrium is reached, the saturated vapor 
must exert the pressure corresponding to the temperature of the 
space occupied. Until this equilibrium is attained, any vapor 
present must be superheated vapor because the number of mole- 
cules in a given space is less than would be the case if the space 
were filled with saturated vapor. Superheated vapor, however, 



Il6 HEAT-POWER ENGINEERING 

exerts a pressure less than that exerted by saturated vapor at 
the same temperature. 

It follows that the pressure under which the liquid changes to 
vapor must constantly increase until a maximum is reached, 
when the space becomes filled with saturated vapor. After that, 
there can be no further change in the relative quantities of 
liquid and vapor present unless temperature changes. 

(d) Since heat is required to change a liquid to a vapor, a 
supply of heat must be obtained from some source to cause 
" evaporation." If heat is not supplied from external sources, 
it is taken from the liquid and surrounding matter; hence the 
sensation of cold when alcohol, or other volatile liquid, is quickly 
evaporated from the skin. 

The actual amount of heat necessary for evaporation may be 
found by considering the process after equilibrium is attained. 
Every pound of dry saturated vapor must have associated with 
it the total heat X corresponding to the existing pressure and 
temperature. 

(e) Usually the space into which the vapor passes contains 
other material beside the vapor; for example, some air is almost 
always present. Dalton's law states that each constituent of 
such mixtures behaves as though the others were not present. There- 
fore, the phenomenon is not in any way complicated by the 
presence of any number of other vapors and gases. The evapo- 
ration goes on until the space is filled with the saturated vapor 
of the liquid in question, and only then is equilibrium reached. 
The vapor will then have all the properties given numerically 
in its vapor table opposite the existing temperature. 

The reason for calling vaporization as first considered a limit- 
ing case of what is generally known as evaporation should now 
be evident. The apparatus used in explanation was so arranged 
that the space available automatically increased as saturated 
vapor became available to fill it. This was done for simplicity 
and because of the close resemblance to the process taking place 
in the steam boiler, from which the vapor is withdrawn as 
rapidly as it is generated. 

Note that the final conditions are the same in either case. A 
certain space is filled with saturated vapor of a given material, 
and what is true of that vapor in one case is true in the other. 

When a space is thus filled with the saturated vapor of a 



VAPORS 117 

material, it is said to be saturated with that vapor or with respect 
to that vapor. Because of a peculiar construction of this ex- 
pression an incorrect idea has become fixed in engineering 
language. It is usual to speak of air saturated with water vapor, 
whereas the real meaning is that a space occupied by air is also 
occupied by saturated water vapor. 

(f) Dalton's law is sometimes called the Law of Partial Pres- 
sures. From the previous statement of this law it is evident 
(i) that when several gases and vapors occupy a space in common, 
each behaves as though the others were absent, and (2) the pressures 
upon the walls enclosing the space, or at any point within the space, 
must be the sum of the pressures exerted by all the constituents of 
the mixture. This pressure is called the total pressure of the 
mixture, while the pressures due to each of the constituents are 
called partial pressures. 

If each constituent may be considered as obeying the laws of 
ideal gases, the same is true of the mixture. The pressure in the 
vessel, then, would be the total pressure, the volume would be 
that occupied by the mixture, and the temperature would be 
that of the mixture, which temperature must be the same for all 
constituents. 

When some of the constituents of such a mixture are satu- 
rated vapors, the perfect gas laws cannot ordinarily be used if 
great accuracy is desired. When, however, the quantity of 
such vapors is small as compared with that of the gases present, 
the error resulting from the use of the gas laws is small, and for 
the sake of simplicity those laws are generally used and the error 
is neglected. 

73. Boiling. Heat is often added to a liquid at such a rate 
and in such a way that the temperature of one part becomes 
higher than the temperature of adjacent parts; that is, local 
heating takes place. This is the result when the local addition 
of heat exceeds the rate of heat conduction through the material. 
Such heating raises the temperature locally to that of vaporiza- 
tion corresponding to the pressure, after which further addi- 
tion of heat would cause local vaporization; that is, a small 
amount of the liquid inclosed within the rest would be converted 
into vapor and appear as a bubble. 

The pressure at any point within a liquid at rest must be that 



Il8 HEAT-POWER ENGINEERING 

due to the static head of the Hquid above that point plus the 
pressure due to any material resting upon the surface. Therefore, 
the bubble of vapor would be formed under that pressure and, 
during formation, would have to displace the column, or 
" piston," of water above it against that pressure. 

The bubble, being less dense than the surrounding liquid, 
would rise, but if the temperature of the liquid encountered was 
lower than its own it might entirely condense before reaching 
the surface. This process continued long enough would bring 
all the liquid approximately to the same temperature, after which 
the vapor bubbles could travel upward through the liquid and 
escape as vapor from the surface. 

Liquid is said to be in a state of ebullition or to be boiling: 
when it is in such a state that bubbles of vapor formed within 
its mass pass up and out through its surface. 

From what has preceded it can be seen that this process will 
occur when the body of water is at such a temperature that the 
pressure of its saturated vapor is equal to that upon its surface. 
This is sometimes given as a definition of boiling temperature. 

74. Temperature-Entropy Changes of Vapors, (a) All the 

processes described in connection with the formation of vapor 
are thermodynamically reversible; hence for vapors, just as was 
done for gases in Section 38 (a), d'E may be substituted for APdV 
in the general Eq. (53) defining an infinitesimal entropy change. 
Then for such a change in a unit weight of vapor the expression 
becomes 

,^ dS + dI + dE . . 

^0 = J , (104) 

or 

^</>=^, . (105) 

and for a finite change 

A* = ff (.06) 

These expressions may be used for determining the entropy 
changes for unit weight of any vapor when undergoing any 
reversible processes. 

(b) The reversible temperature-entropy changes occurring 
during the vaporization of water at several different pressures 
are shown graphically in the T(^-diagram given in Fig. 33. 



VAPORS 



119 



During the heating of the liquid at constant pressure the 
specific heat Cp, or heat required per pound per degree, may be 
either variable or constant. The equation for the lines ab, 
abi, abi, etc., for the entropy change experienced by the liquid^ 



000 






f 


% 








\ 


l\ 






h 


^J 








\e3 


-4 


3/ "; 


1™ 

9^ 


/ 




150 Lbs 




\e2 








/ 




70 Lbs 




V: 


\j 


f- 


h 

m 
a 


X 






30 Lbs 








v 


/ 








10. Lbs 




Sat 


iration 


o..'|\ 


/ 





















0,2 0.1 O.C 0.8 1.0 .1.2 .1.1 1.6 1.8 

Entropy 
Fig- ^Z- — T^-Diagram for Water and Water Vapor. 

called briefly the entropy of the liquid, must be the same as 



Eq. (61) and is 



A0^ 



=r 



C^dT 



A0; = Cplog 



(107) 



(108) 



This last equation can bejised even if the specific heat is not 
a constant, by interpreting Cp as the mean value over the given 
temperature range. 

(c) The process of vaporization is a constant-temperature or 
isothermal one; here, following Eq. (65), the entropy change 
experienced by the material during vaporization, called briefly 
the entropy of vaporization, is evidently 

^"^'^T^^Y, ^^^9) 

where Tv is the temperature of vaporization. 

(d) During superheating of the vapor at constant pressure 
the specific heat may be either variable or constant, and, parallel- 
ing Eq. (61), the entropy change, called briefly entropy of super- 
heating, is . 

*" ''Jr. ~^ ^"°^ 

* It is usually more convenient to use logio instead of loge. Since loge = 
2.302 logio, Eq. (108) maybe written Ai^^ = Cp X 2.302 logio {T2/T1). The other 
logarithmic equations which are to follow may be similarly transformed. 



I20 HEAT-POWER ENGINEERING 

A0Z) = Cploge 7fr = Cploge 7f^ — , . . . (i loa) 

where Cp is the mean specific heat, D is the temperature in- 
crease above the saturation temperature, Tv, and T^ = Tv -\- D. 

(e) Summing up these results gives the total entropy change 
experienced by the material when transformed at constant 
pressure from liquid at datum temperature to superheated 
vapor at temperature (/„ + D). This, which is briefly called 
the total entropy of superheated vapor, is 

A(/)s = A<^i + A</)„ + A(/)^ (ill) 

Then A^. = j^^ ^^+-+j^^ -^ . . (112) 

= Cp loge ^ + i=r + Cp loge ^^p^ , . (l 12a) 

in which To is the datum temperature, Tv is the temperature of 
saturation, and Ts {= Tv -\- D) is that of the superheated steam 
when the amount of superheat is D degrees. 

(f) If vaporization ceases before the entire pound of material 
has been vaporized, only a part, xr, of the total latent heat of 
vaporization, r, will have been added. The entropy change 
experienced by the material in coming to the condition of wet 
saturated vapor with quality x would then be 

A<i)^ = ^(j)l + x^(j)y (113) 

— X'v XT 

^ CpXoge jr + TfT (114) 

I I V 

When X becomes unity, — that is, when vaporization is just 
complete, — there is dry saturated vapor, and this equation 
becomes 

A(j)sa = Acjil -\- Acl>v (115) 

— Tv r 

= Cploge -TfT -{--7^ (116) 

I J- V 

The points e, ei, 62, etc., in Fig. 33, show the entropy change 
for different pressures as determined by Eq. (114) when x = 0.75. 
Obviously the distances he, hiCi, etc., must be 0,75 of the dis- 
tances he, hiCi, etc. This diagram then furnishes a means of 
determining quality in a manner similar to that used in the case 
of the saturation curve, Fig. 32, but is not subject to the ap- 
proximation there necessary. 



VAPORS 121 

75. Continuity of the Liquid and Gaseous States, (a) It has 
been stated, in Chapter IV, that no real gases obey exactly the 
laws of ideal ones, but that it may be assumed without great 
error that those real gases which are farthest removed from the 
conditions of liquefaction do obey these laws. This assumption, 
however, is not justified at 
very low temperatures or 
very high pressures. 

The study of materials in 
the liquid and gaseous spates 
shows clearly that these 
states are in the nature 
of limiting conditions to 
gradual physical changes. 
This may be presented by 
means of Fig. 34. It should 
be clearly understood how- 
ever that this figure is 
qualitatively but not quanti- 
tatively correct; that is, it is 
not drawn to scale, nor does 
it exactly represent the be- 
havior of any real material. 
It does, however, show the 
nature of the changes under 
consideration for all known 
materials. 

(b) The diagram is for unit weight of material on pressure- 
volume coordinates, and each of the heavy lines is an isothermal. 
Starting with the lowest line of the series, the point a represents 
the volume occupied by unit weight of liquid at temperature T 
and at the pressure shown. If the pressure is decreased while 
the temperature is maintained constant, the volume of the 
liquid will increase until the point h is reached.* At this point 
the pressure, volume, and temperature are such that any further 
change can only be a progressive vaporization at constant pres- 
sure, as shown by line be (since the temperature is constant) with 
increase of volume from h to c; that is, the material is at the 




Specific Volumes 



Fig. 34. — Isothermals of Material in Liquid^ 
Vaporous and Gaseous States. 



* The increase of volume has been much magnified in the figure to emphasize 
the phenomenon. 



122 HEAT-POWER ENGINEERING 

point of vaporization for temperature T. At c the material has 
become fully vaporized, and hence is dry saturated vapor. A 
further decrease of pressure at constant temperature will cause 
it to become superheated and to behave somewhat like an ideal 
gas. The volume will then increase almost inversely with the 
pressure, bringing the material to the conditions d along the 
curve cd. 

Starting from ai, with the material in liquid form at a tem- 
perature Ti > T, a. similar process carries the material isother- 
mally to di. The same statements can be made for all other 
starting points at different temperatures up to some such value 
as Tz, when the process will be that shown by the curve asb^ds. 
In this case the points bs and C3 have become coincident, the 
liquid, if it is such, having the same volume at pressure Pbs as 
does its vapor. 

At higher temperatures, such as Ti and T5, the material begins 
as a gas and the isothermals become more and more nearly 
rectangular hyperbolas {PV = const), as they are drawn for 
higher and higher temperatures. 

Reversing the process, a gaseous material compressed iso- 
thermally from d^ conditions will remain gaseous no matter how 
high the pressure is carried. A gaseous material compressed 
isothermally from di will, however, begin to condense at Ci and 
will continue to liquefy with further compression until it all 
becomes liquid at bi. 

(c) If ds is chosen as the point to begin isothermal compression, 
it is obvious that the material after passing b^ must be on the 
boundary between the liquid and gaseous states; that is, the 
pressure, volume, and temperature conditions for the two states 
are the same and the material may be considered a liquid or a 
gas, or both. 

The conditions at bs are called critical conditions, that is, 
critical volume, critical pressure, and critical temperature. The 
critical temperature of gaseous material is usually defined as the 
temperature above which liquefaction is impossible by any 
increase of pressure. The truth of this definition is evident from 
the diagram; no isothermal of higher temperature than azbzd^ 
could cross the latter and so enter the liquid region. 

(d) In the figure the hatched area with the lines running 
upward from left to right represents the region in which the 



VAPORS 123 

material must be liquid. That is, when any point representing 
the pressure and volume of the substance falls within this region, 
the material must be in the liquid state. Similarly, the part 
hatched downward from left to right represents the region of 
superheated vapor, and that crosshatched in both directions 
represents the region of liquid mixed with its saturated vapor. 

The part not hatched represents the region in which the 
material cannot be liquefied by change of pressure. This is 
now commonly called the region of the gaseous state. A gas 
may then be defined as a material above the critical temperature, 
and a vapor as material which, while resembling a gas, is below 
the critical temperature. 

It must not be inferred that material above its critical tem- 
perature sensibly obeys the laws of ideal gases. It must be far 
removed on the temperature scale before this occurs. The 
isothermal T5 shows this. 

Note in the figure that the curve bse is the saturation curve, a 
part of which was drawn for water vapor in Fig. 32. 

(e) This diagram. Fig. 34, is useful for determining the be- 
havior of material when subjected to volume, pressure, and 
temperature changes. Material in the gas state, as at / for in- 
stance, can be liquefied by lowering temperature and decreasing 
volume while the pressure is maintained constant, as along the 
line fg. Or it can be brought to the condition of wet vapor by 
lowering pressure, volume, and temperature according to some 
curve fh. Similarly, increasing the temperature and pressure of 
a superheated vapor at constant volume (line kl) results in 
carrying it into the gas field. 

(f) At the critical temperature the latent heat of vaporiza- 
tion, r, becomes zero; that is, no internal and no external work 
of measurable magnitude is done, as the material passes from 
just above to just below the point bs on the isothermal T3. In- 
spection of the Steam Tables in the Appendix will show the way 
in which the latent heat of vaporization of water vapor gradually 
decreases from large values at low temperatures to a value of 
zero at the critical temperature. 

76. Van der Waals' Equation for Real Gases, (a) Obviously 
any gas is really only a very attenuated liquid, differing in its 
properties from the liquid because its molecules are much farther 



124 HEAT-POWER ENGINEERING 

apart, and possibly of simpler structure. If this is true, it ought 
to be possible to write laws of condition which would fit the 
same material in either the liquid or the gaseous form. Several 
attempts have been made to do this, and one in particular is of 
great interest. It is due to Van der Waals and was developed 
by modifying Boyle's law to take account of two assumed facts. 
These are: 

(i) The space filled by a gas is partly occupied by the mole- 
cules of that gas, and it is only the space between the molecules 
which obeys Boyle's law. 

(2) In no real gas are the molecules far enough apart to be 
absolutely independent of one another; certain intermolecular 
forces still exist. These decrease the total volume occupied or 
make the gas behave as though subjected to a pressure greater 
than the real external pressure. 

The law in mathematical form is 

P+^\(Y -b) = Constant, 

(p+~j{Y-b)=RT, (117) 

in which a and b are constants, differing with the kind of gas. 
(b) This equation can be rearranged to read 

V-V^(^H-6) + v|-|^ = o,. . . (.18) 

a cubic equation in terms of the specific volume V. Then for a 
given temperature and pressure there must be three values of V 
which satisfy the equation. 

If the curves obtained by substituting in the equation are 
drawn for constant temperatures, they resemble the lines abed, 
etc., in Fig. 34, except that the horizontal lines be, etc., are re- 
placed by the dotted curves shown. If the equation is really 
true, the process of vaporization must be more complicated than 
at first appears. The fact that the phenomena corresponding 
to part of the curve from b downward and from c upward can 
be realized experimentally gives evidence in support of this law. 
The condition of the material thus carried into the dotted 
position of the curve is, however, very unstable, and the sub- 



VAPORS 125 

stance suddenly assumes the condition shown by the horizontal 
line if disturbed. 

(c) The critical point may now be said to be the point at 
which all three roots of the equation coincide or at which one is 
real and two are imaginary. 

(d) The equation of Van der Waals, though better than that 
of Boyle, does not fully express the truth. If it did, it would 
hold for material in the solid as well as in the liquid state. It 
really recognizes no such condition as solid. If it did, its graph, 
continued far enough back in the direction dcba, would show 
another jog similar to but shorter than cb, representing the con- 
stant-pressure, constant-temperature change from liquid to solid. 
This it does not do, and hence it is Imperfect. 

(e) The phenomenon of zero volume at absolute zero tem- 
perature can now be explained. According to the simplest 
kinetic theory of gases, the temperature is supposed to be a 
measure of the translational energy of the molecules, and the 
pressure is the result of the bombardment of containing walls by 
the rapidly moving molecules. 

Assuming, with Van der Waals, that the volume to which the 
ideal laws refer is not the total volume occupied by the gas, but 
equals that volume corrected for the volume of the molecules 
present, the limiting case of the ideal laws is easily explained. 
When absolute zero of temperature is reached the molecules of a 
gas must be assumed to be devoid of translational motion and 
in such positions that the volume referred to above has become 
zero. Then as the molecules at rest could not bombard sur- 
rounding surfaces the pressure would also be zero. 

This equation of Van der Waals is In general only of theoretical 
interest to the engineer. Seldom does the accuracy required in 
engineering calculations warrant the use of such refinement. It 
is introduced here only to give a possible simple explanation, 
though an incomplete one, of what otherwise seems very in- 
definite, and to furnish a more complete view of the continuity 
of the liquid and gaseous states. 



CHAPTER X. 

PROPERTIES OF STEAM. 

77. Steam or Water Vapor. (a) All that has just been 
said about the formation and the properties of vapors in general 
applies, of course, to the case of water vapor or steam. 

This vapor is usually generated in a boiler in which the pres- 
sure is maintained substantially constant by the withdrawal of 
some of the steam as rapidly as more vapor is generated. This 
withdrawal occurs ordinarily through the steam pipe, at other 
times through the safety valve. The water when pumped into 
the boiler is under the pressure existing in that vessel. Thus 
the application of heat causes the temperature of the liquid 
to rise under constant-pressure conditions. This increase of 
course ceases when the temperature of vaporization, correspond- 
ing to the pressure, is reached. Since the heat is added at con- 
stant pressure, g would be computed from Eq. (94), using the 
mean specific heat at constant pressure for Cp. 

(b) The further addition of heat to this water causes the 
formation of vapor, or steam. Associated with this process there 
is great increase in volume and the absorption of large amounts 
of heat. In discussing the general case, in connection with 
Fig. 30, it was considered that the external latent heat expended 
in connection with the volume-increase was utilized in lifting a 
weight, thus doing work in overcoming the action of gravity. 
In the case under consideration, when steam is supplied to a 
piston engine, the external latent heat is expended in displacing 
the piston against resistance, thus doing external work equal to 
APu per pound of material and making available increased 
volume of steam space in the cylinder as rapidly as the vapor is 
generated. It is true that engines of this type ordinarily take 
steam intermittently from the boiler, hence the steam pressure 
within that vessel would fluctuate slightly on this account, even 
if other causes of fluctuation could be eliminated. In such cases 
the mean pressure is the one commonly used. 

126 



PROPERTIES OF STEAM 127 

It is not only true in the case of the piston engine but also in 
all other cases, that the withdrawal of steam from the boiler is 
accompanied by the doing of external work, equal to APu per 
pound of material, although just how this energy is expended is 
not always clear to the beginner. 

The rest of the heat utilized in the process of vaporization is 
the " internal latent heat," p, expended in causing the molecular 
rearrangement accompanying the change from water to steam. 

(c) In many instances a portion of the steam pipe is modified 
in form and subjected to heat in such manner that it becomes 
what is termed a " Superheater," in which the steam becomes 
superheated by the reception of more heat, as it passes through, 
on its way to the engine or other device which is being supplied. 
During this superheating the steam is under constant pressure, 
hence in using Eq. (102) to determine the heat added the mean 
specific heat at constant pressure Cp should be introduced. 

78. Sources of Data. The different related properties of dry 
saturated steam are tabulated in Steam Tables such as that 
given in the Appendix. Some of the properties are determined 
directly by experiment and others are derived quantities which 
are found by computations involving the experimentally de- 
termined data. 

Many different Steam Tables have appeared, and all except 
the most recent ones were based on Regnault's experiments, 
published in 1847. These older tables, while thus based on the 
same data, depart somewhat from one another in the values 
tabulated, the disagreement arising from differences in inter- 
preting the data and in choosing values of Joule's equivalent, 
absolute zero, specific heat of liquid, etc. 

In spite of their differences and errors, these steam tables are 
still sufficiently accurate for most engineering calculations; and 
ordinarily the results of investigation which involved their use 
may be compared with those based on the later tables, without 
introducing serious errors. 

The recent rapid increase In the use of superheated steam has 
led to many attempts to determine accurately the different 
values of the specific heats of this material under various con- 
ditions. This has revived Interest in the properties of saturated 
steam, with the result that in 1909 new and more accurate Steam 



128 HEAT-POWER ENGINEERING 

Tables appeared in book-form, one by Peabody, and another by 
Marks and Davis. Both books, besides giving tables for the 
properties of dry saturated steam, contain elaborate tables giving 
the entropy and other properties of superheated steam, and other 
auxiliary tables, together with certain charts which are useful to 
the engineer. 

For the mechanical equivalent of i B.t.u., Peabody uses 778 
foot-pounds and M. & D. use 777.52. For the absolute zero the 
former uses 491.5° F. below freezing; the latter 491.64. Peabody 
uses for the B.t.u. the heat required to raise one pound of water 
from 62° to 63° F.; whereas M. & D. use the "mean B.t.u." 
defined in Section 3.* The values chosen for the specific heats 
of water also vary slightly. However, the differences mentioned 
are so small as to be negligible for engineering purposes. 

The discussion of how tables may be made will now be taken up 
very briefly. For a more thorough treatment and for references 
to the sources of data the student is referred to the books just 
mentioned.! 

79. Properties of Dry Saturated Steam. The properties 
given in the Steam Table in the Appendix are the corresponding 
values of (a) Pressure and Temperature; (b) Heat of the Liquid; 
(c) Total Heat of Steam; (d) Latent Heat of Vaporization; (e) 
External Latent Heat; (f) Internal Latent Heat; (g) Entropies 
of Water, Vaporization, and Total; and (h) Specific Volumes. 

The properties are tabulated for one pound of material, the 
pressures are in pounds per square inch absolute, and the heat 
quantities and entropies (excepting those for vaporization) are 
measured above 32° F. 

Temperatures and Pressures. 

(a) It has been seen that saturated vapor has a definite tem- 
perature corresponding to each pressure at which the vaporiza- 
tion occurs. The variation of temperature with pressure of 
water vapor has been determined experimentally and is shown 
graphically in Fig. 35, to two different pressure scales. It is 
important to note the shape of this curve, especially the rapid rise 

* The mean B.t.u. is about ^^g larger than that measured at 62°. 
t Also see Trans. A. S. M. E., Vols. 29 to 33, for papers, discussions, and refer- 
ences to sources. 



PROPERTIES OF STEAM 



129 



dp 
of pressure, or increase in the slope -77 with elevation of tem- 
perature in the upper region. The TP relations can also be 



A 

300 

|250 

1^00 


B 






















/ 




/ 








■71 














1 


A 


i 


4 

SlOO 








/ 


dp 


/ 








/ 


/ 




/ 




s.. 


dt 




• 




y 


^,,' 


y 







100 200 300 400 500 600 700 

•Temperatures Deg.Eahr. 

Fig- 35- —PT Relations for Steam. 

expressed algebraically by formulas* which are rather compli- 
cated. These need not be given here, however. 

Heat of Liquid (g). 

(b) The heat of the liquid is the amount added to water at 
32 degrees in order to bring it to the temperature of vaporiza- 
tion. Its amount is computed by using Eq. (92) and integrating 
between the temperatures of freezing and of vaporization, thus: 

2=1 Cpdt = j CpdT, . . . . (119) 

J 32 J 492 

where Cp is the constant-pressure specific heat of the liquid, 
which in the case of water varies with the temperature. The 
progressive values of Cp have been found by several experimenters 
with results that are not absolutely in accord. The curve in 
Fig. 36 represents an interpolation between the several data. 

The right member of Eq, (119) will be recognized as the ex- 
pression for the area below the Cp curve, and lying between the 
ordinates at 32 degrees and /„. This area can be found by 
planimeter or other method of integration. 

* See "The Pressure-Temperature Relations of Saturated Steam," by Prof. 
Lionel S. Marks. Trans. A. S. M. E., Vol. 33. 



130 HEAT-POWER ENGINEERING 

If Cj, is the Mean Specific Heat for the temperature range 
d — {tv — 32), between limits 32 degrees and tv, then 

g_ = Cj,{t-Z2) = Cj,Xd (120) 

Cp is obviously the mean height of the part of the Cp-curve 
lying between the temperature limits under consideration. 



a.i8 

1.16 

1.11 












1 


r 












/ 






Water 








/ 




m 1.10 
|l.OS 

1 '•'' 

pi 1.02 
1.01 
1.00 
.99 
,98 










/ 


/ 












/ 














/ 














/ 














/ 


/ 








\ 






/ 












s 


^^ 


1/ 






v.. 














J 











Fig. 36. 



Temperatures Deg. Fahr. 
Progressive Values of Specific Heat, Cy, of Water. 



Hereafter the instantaneous, or the progressive, values of C^ 
(that is, those corresponding to one degree rise at different tem- 
peratures) will be called the progressive specific heats to dis- 
tinguish them from the mean values. 

For many purposes, especially at low temperature, it is 
sufifiiciently accurate to assume Cp = i, then g = (/ — 32). In 
computing the values of g for the steam tables, however, it is 
necessary to employ the greatest accuracy. 

In Fig. 31, the curve abz shows approximately how g varies 
If Cp is taken as unity, this curve becomes a straight 



with U 
line. 



Total Heat of Steam (X). 



(c) This is the amount of heat required to raise one pound of 
water from 32 degrees to the temperature of vaporization, then 
to separate the constituent particles during the formation of 



PROPERTIES OF STEAM 13 1 

steam, and to do the external work accompanying the increase in 
volume. 

The values of X have been determined for a number of pressures 
by various experimenters. By plotting the most trustworthy 
data on cross-section paper, with X and temperature as coordi- 
nates. Dr. H. N. Davis obtained a curve which is generally 
regarded as giving the most reliable values of this quantity. 
The portion of the curve lying between 212 degrees and 400 
degrees is represented by the equation 

X = II5O.3 + 0.3745 {tv- 212) - 0.00055 {iv- 212)2. (J2I^; 

Regnault's formula for total heat, which was generally em- 
ployed before 1909, is accurate enough for ordinary engineering 
purposes and is much simpler than Davis'. It is 

X = 1091.7 +0.305 (^^,- 32). . , . (122) 

Note that this quantity increases with the temperature, but at 
a very slow rate. This is shown in Fig. 31, by the abscissas of 
points c, ci, C2, etc. The higher the pressure the less rapid is 
the rate of increase. 



Latent Heat of Vaporization (r). 

(d) Having obtained the total heat X and the heat of the 
liquid 2) the latent heat of vaporization may be found from 

r = \- q (123) 

If the specific heat of water is taken as unity, q = (tv — 32) ; 
and if this is subtracted from Eq. (122), Regnault's approxi- 
mate equation for the latent heat of vaporization is obtained. 
This is 

r = 1091.7 - 0.695 (/„ - 32) (124) 

In Fig. 31, the values of r for different temperatures and pres- 
sures are shown by the distances be, h^ci, hzCz, etc. The latent 
heat decreases with rise in temperature, and becomes zero at the 
critical temperature. At atmospheric pressure r is 970,* and 
this figure should be remembered, as it is used frequently ia 
engineering computations. 

* The old value is 966. 



132 HEAT-POWER ENGINEERING 

The External Latent Heat (AE). 

(e) The external latent heat A£ expended in displacing the 
surrounding media can be computed from the equation 

^^ = ^^^=H4Apu = APu, . . . (125) 

in which A = — -' p is the pressure in pounds per square inch, 

P is the pressure in pounds per square foot, and u is the increase 
in volume during vaporization. How u may be determined will 
be explained in (h) of this section. The value of APu is rela- 
tively small and varies from about 61 B.t.u. at one pound 
pressure to about 85 B.t.u. at 400 pounds. 

The Internal Latent Heat (p). 

(f) The internal latent heat expended in producing the molec- 
ular rearrangement may be obtained by subtracting the external 
latent heat from the total. Thus 

p = r -APu (126) 

Entropies (A0). 

(g) The values tabulated are per pound of steam. The 
entropy of the liquid may be found from 



A0, 



= / ^ = Cp\ -r (127) 

t/492 J 1/492 -t 

As the heat of the liquid, Cp j dT, is measured above the freez- 
ing point of water, it follows that the corresponding entropy 
must also be calculated above the same datum, that is, 492*^ F. 
absolute. The integration of Eq. (127) gives for the entropy of 
water, 

A0, = Cplog,^, (128) 

in which Tv is the saturation temperature for the pressure under 
consideration and Cp is the mean specific heat of water for the 
temperature range from 32 degrees to tv, as found from Fig. 36 
in the manner described in Section 79 (b). 

The entropy of vaporization (A0„) may be found from Eq. 



PROPERTIES OF STEAM 



[33 



(109) by substituting the values of Tv and r corresponding to 
the pressure under consideration. 

The total entropy (A^^a) of one pound of dry saturated steam 
above 32 degrees is A(/)ga = A^^ + A^,,. 



Specific Volume (V). 

(h) This is the number of cubic feet occupied by one pound of 
steam. It varies with the pressure and is equal to the sum of 
the original volume of the pound of water (0.017 =t cu. ft.)* 
and u, the increase in volume during vaporization. Thus, 

V = w + 0,017 ± cu. ft (129) 

The value of u can be obtained from what is known as Clapey- 
ron's equation, 

= j: 221 



[dtj 



cu. ft. 



(130) 



Here (-77) is the slope of the pressure- temperature curve 



dp 



see Fig. 35, in which -^ 



Wt)' ^"^ "^^^ ^^ found either 

graphically or mathematically. 

The following is a rather crude way of deriving Clapeyron's 
equation: On a PV-diagram, Fig. 37, starting at A with one 




Fig. 37- 



Fig. 38. 



pound of water already at the boiling point (pressure P, and 
absolute temperature T), let sufficient heat be added to cause 
complete vaporization, the increase in volume being u; then let 
there be a slight drop in pressure dP, next let there be a de- 

* The volume of a pound of water varies from 0.016 to 0.018 cubic feet within 
the ordinary range of temperatures. 



134 HEAT-POWER ENGINEERING 

crease in volume at the uniform pressure (P — dP) until all of 
the steam is condensed to water at the corresponding boiling 
point; and finally bring the water up to its original temperature 
to complete the cycle. Evidently the work done, as shown by 
the area of the figure, is u . dP foot-pounds, which in B.t.u. is 

U'dP , . 

^^ = ^w ^"' 

On the T</)-diagram, Fig. 38, let the same cycle be shown. 
Starting at A with water at the boiling temperature T, let heat, 
r, be added to vaporize the water. This is accompanied by an 

T 

increase in entropy of amount y. Next let there be a temper- 
ature drop dT (corresponding to dP), and then let the steam 
be condensed at constant temperature (2" — dT), corresponding 
to (P — dP), to water at the boiling point. Upon returning the 
water to its original condition the cycle is completed and the 
work done in B.t.u., as shown by the area surrounded, is 



^E 



= {^dT (b) 



Evidently equations (a) and (b) both represent the same 

amount of work. Hence, — — = {-TpAdT, solving which for u 
778 \T) 

results in Clapeyron's equation. 

The Specific Density. 
(i) The specific density or weight of one cubic foot of steam is 
equal to f:^j. As this is merely the reciprocal of the specific 
volume, it is not given in the Steam Table in the Appendix. 

Properties of Steam at High Pressures. 

(j) Above 250 pounds per square inch (400° F.) the properties 
of steam have not been determined with great accuracy, so that 
the values given in the tables above this pressure are not very 
trustworthy. More accurate values are, however, not available 
at present. 

It will be noticed that the latent heat decreases as the tem- 
perature increases until it becomes zero at the critical tempera- 



PROPERTIES OF STEAM 



^35 



ture of about 706° F.,* corresponding to a pressure of about 
3200 pounds per square inch, 

80. Properties of Superheated Steam, (a) Specific Heat at 
Constant Pressure. In dealing with superheated steam the 
engineer ordinarily uses only the specific heat at constant pres- 
sure. For ideal gases it has been shown that Cp is independent 
of temperature and pressure, and that it is sensibly so for most 
real gases within ordinary ranges. For superheated steam, 
however, it cannot be considered constant at the temperatures 
used in engineering, for the material is always far below the 
critical conditions, and though approximating the behavior of 
a gas it varies greatly from the laws for perfect gases. 

Several experimenters have recently determined values of Cp 
for steam over wide temperature and pressure ranges. Among 
these the results of Knoblauch and Jakob are generally con- 
sidered the most trustworthy, and were used both by Peabody 




Fig- 39- 



Temperatures Deg. Fahr. 
Progressive Values of Specific Heat Cp of Superheated Steam. 



and by Marks and Davis in computing their tables. M. and D. 
made slight modifications to better coordinate the Knoblauch 
and Jakob results with those of other authoritative researches. 
The variation of the progressive specific heat Cp with tempera- 
ture, for different constant pressures, is shown in Fig. 39. Be- 
* Prof. L. S. Marks. Trans. A. S. M. E., Vol. i^. 



136 



HEAT-POWER ENGINEERING 



cause of the comparatively rapid variation from degree to degree, 
the progressive values can be used in ordinary arithmetical cal- 
culations for a temperature rise of one degree only. 

For greater ranges, the mean specific heat must be used, and 
this can be found from Fig. 39 in a manner similar to that 
described in 79 (b) for the mean specific heat of water. As most 
problems connected with superheated steam involve a tem- 
perature range D measured from the saturation temperature, T^, 
for the pressure under consideration, it is convenient to have 



.40 



v\ 


\\ 


\ 


Superb 


ated Ste 


m 


\ 


\\ 


\^ 


\*. 






\^' 


x\' 


\^ 


^"^ 


V.., 




N 




>:i' 






"^^ 




■---^ 




^^ 


' ^ 


^-^- 


, , 


^ 


_50 


' — • . 


_^^^2 


^^^iizz: 




" 






15 













1 





















50 100 150 200 250 

Temperatures above Saturation "F. 



Fig. 40. — Variation of Mean Specific Heat Cp of Superheated Steam. 



curves giving the constant-pressure mean specific heat Cp 
measured above saturation temperature. The values plotted in 
Fig. 40 may be used pending the appearance of more accurate 
ones. 

Superheat. 

(b) The heat added during superheating D degrees is evidently 

A(2/> = CpD • • • • (131) 

where D = (Tsup — T^). 



PROPERTIES OF STEAM 137 

The Total Heat of Superheated Steam (A<2a). 

(c) This quantity is the total heat above 32° F. per pound of 
steam which is superheated D degrees above saturation tem- 
perature. Representing this by A(2s, it is given by the equation 

^Qs = \ + A(2^ = X + CpD (132) 

The Entropy of Superheated Steam. 

(d) The entropy above saturation temperature T^ is A0/) and 
is given by Eq. (no). 

The total entropy of steam superheated D degrees is obtained 
from Eq. (in) or (112). 

Specific Volume of Superheated Steam (V,). 

(e) The volume of one pound of superheated steam may be 
computed from Linde's empirical formula 

T 
Vs = 0.5962- - (i + 0.0014^) 
P 

^y /i50,300,ooo „ \ , . 

X[ \z 0.0833J, . . . -(133) 

in which Vs is in cubic feet, T is the absolute temperature of the 
superheated steam in Fahr. degrees, and p is in pounds per 
square inch. 

A simpler formula and one that is nearly as accurate is given 
by Tumlirz. It is, for p in pounds per square inch, 

T 
Vs = 0.5962 - - 0.256 (134) 

and for P in pounds per square foot, 

V. = 85.86^-0.256 (135) 

81. Temperature-Entropy Chart for Water and Steam. 

(a) Diagrams drawn with T^-coordinates are of great con- 
venience in solving many problems involving the use of steam. 
Especially are they valuable when reversible adiabatic changes 
and associated heat changes are considered, for with these co- 
ordinates, the former are straight lines and the latter are areas. 

The T(/)-chart may be constructed for any weight of working 
substance ; but it is customary and more convenient to base it on 



138 



HEAT-POWER ENGINEERING 



unit weight. The chart in Plate I in the Appendix is for one 
pound and the entropies are measured above 32° F. to corre- 
spond with the steam tables. 

The value of a T<^-chart is greatly increased by the addition 
of certain lines of reference which aid in reading directly many 
of the quantities sought. The construction of these lines will 
now be considered. 

Water Curve, or W-curve. 

(b) Eq. (128) expresses algebraically the law by which the 
entropy of the liquid varies with the absolute temperature. 
From it can be obtained simul- 
taneous values of 3"^ and A^^ and 
these can be used in plotting 
points on a 2"(/)-chart to show 
graphically the relation between 
the two variables. The Water 
Curve is the locus of these points 
and therefore is the graph of Eq. 
(128). In Fig. 41, AB is the 
W-curve. 

If a steam table is available the 
values of A0i and /„ used in plot- 
ting the W-curve can be obtained 
directly from it. 
In general the heat used during a reversible process to pro- 
duce a r^-change is 



-A <!>-»-(<- A ^ 




Fig. 41. 



■ T0-Diagram for Water 
Vapor. 



A<2 



r 



Td4>. 



The right side of this equation is of the form / y dx, which is the 

mathematical expression for an area, and which here represents 
the heat quantities AQ. As dx in this case is dcf), which is 
measured above 32° F., the heat represented by the area must be 
that above 32° F. also; and as y = T (abs) these areas must 
extend down to absolute zero of temperature, that is, to the <^-axis. 
From this it is seen that the heat of the liquid above 32° F. is 
represented by the area under the W-curve, extending to the 
T and axes, such as area 0AB4>i, in Fig. 41. 



PROPERTIES OF STEAM 139 

The W-curve has Httle curvature. If it is considered straight 
(as it would be if Cp = const. = 1), it is seen that the area under 
that Hne is the product of A^; by the mean temperature 

^ + 49^ that is, 
2 

q = A(l>i -^^(approx.) (136) 

Substituting q = {T — 492), which would be its value when 
C = 1, gives the following approximate equation for the entropy 
of water : 

A«A^ = 4^p^ (approx.), .". . (137) 

which is convenient for rough computations, as it does not 
involve the use of tables. 

Saturation Curve, or S-curve. 

(c) The entropy of dry saturated steam is, from Eq. (115),. 
A4>sa = A(f>i + A</)„ = A(^i + ^/ T, the values of all quantities in 
which are given in the steam tables. In Fig. 41, the abscissa 
TB is A(t)i for the temperature T; so if BC is made equal to 
the corresponding value of A{/>„, the point C must fall on the 
Saturation Curve. The locus of a series of points plotted in 
this manner for different temperatures is the S-curve. Evi- 
dently this curve is the graph of Eq. (115). 

The area of the rectangle below the line BC is 

Act>,XT = ^XT=r, 

and hence is the latent heat of vaporization. Then the total 
heat of the steam, X, is given by the area below ABC, since this 
latter represents r -{- q. 

Constant- Quality Curves, or X-curves. 

Xf 

(d) The equation of these curves is A(j)x = A(^i + -y; , in which 

X is constant for each curve and is equal to the quality under i:on- 
sideration. Taking various corresponding values of r and T from 

the steam tables, the quantities (-:= j may be computed, and add- 



140 



HEAT-POWER ENGINEERING 



ing these to the values of A0z for the corresponding tempera- 
tures gives A0X. In Fig. 42, TB as before equals A4>i and BD is 




Fig. 42. — T0-Diagram Showing X-Curves. 

laid off equal to ifji thus locating the state point at D for 

the temperature T. The locus of points similarly plotted for 

different temperatures is the Curve of Constant Quality. A 

series of such curves is shown in Fig, 42 (a). 

r xr BD 

Since BC = ^^ and BD = =t' it follows that -^5^ = x. 
1 I ±>C 

This relation suggests another and simpler method of plotting 
points to determine the X-curve: In the figure draw the hori- 
zontal intercepts BC, BiCi, etc., between the W-curve and the 
S-curve, and on them locate the points D, Di, etc., in such 

positions that -^-^ = J J' = etc. = x. Then the locus of these 
nL -DiCi 

points, D, Di, etc., is the curve desired. 

The heat used in vaporizing x parts of a pound of steam at 

temperature T is shown by the area below BD, Fig. 42, since 



this area 



X T ^ xr. The total heat in the mixture of 



steam and water is given by the area below ABD, for this area 
equals xr -}- q. 

Constant-Volume Curves, or V-curves. 

(e) At any temperature T, Fig. 43, the change in entropy 
from B to C during complete vaporization is accompanied by 
an increase, equal to u, in the volume of the working substance. 
If at the same temperature only part of the unit weight — 
occupying the volume F — is in the vaporous form, it is evident 



PROPERTIES OF STEAM 



141 



that the quality of the steam must be x = 



(F-0.017) 



By 



maintaining V constant in this equation and substituting values 
of u corresponding to different temperatures, the way x varies 
with T during an isovolumic change can be determined. Then 
the V-curve can be plotted either by using the quality or by 
making 

BD ^ {V - 0.017) ^lA _ (F- 0.017) 

BC u ' BiCi Ml ' 

The same curve can be obtained by graphical construction in 
the following manner: In Fig. 43 lay off a V-axis opposite to 
the T-axis, thus forming a V0-quadrant 
in which volumes are laid off downward. 
Directly below B drop an ordinate ab 
for the corresponding volume of the 
material. This is the volume of the 
water at temperature T, or 0.017 ± 
cubic feet. Directly below C lay off 
the volume corresponding to that point, 
thus locating c. The value in this case 
is V, the specific volume of the steam. 
Then the straight line be joining these 
points shows the uniform increase of the 
volume and entropy during the process 
of vaporization of one pound of working 
substance at the temperature 2". In 
like manner similar V</>-lines, such as 

biCi, &2C2, etc., can be drawn for other 

r • ^- Tr Fig. 43. — T^-Diagram Show- 

temperatures of vaporization. If any . ,, ,, j t^ ^ *• 

. . . ing Metnod 01 Constructing 

isovolumic line V is then drawn, it inter- V-Curves. 
sects be, biCi, etc., at points v, Vi, v^, etc., 

whence projecting upward to the corresponding isothermals de- 
termines points D, Di, etc., on the V-curve with T(f) coordinates. 
In the case shown in this figure, V = Vi, so Vi would coincide 
with ci, and Di with d. 

Constant-Heat Curves, or Q-curves. 

(f) For wet saturated steam the equation of this curve is 
xr -\- q = const. = AQ. For any given AQ, the variation of x 
with T can be found by substituting the values of r and q corre- 




342 



HEAT-POWER ENGINEERING 



Spending to the different temperatures used. Several of these 
curves for different values of AQ are shown in Fig. 44. Referring 

to curve E E1E2, etc., it is evident 
that the areas under ABE, ABiEi, 
etc., must all be the same and 
equal to the value of AQ for that 
curve. Note particularly that 
these curves represent xr -]- g and 
not xp + 2. 

(g) For superheated steam the 
Q-curve is found in the following 
manner: For any assumed pressure 
p, the corresponding values of X 
and T-e are obtained from the 
Steam Tables. Then if AQ is the 




Fig. 44. — T</)-Diagram Showing 
P-Curves, and Q-Curves. 



constant-heat quantity under consideration, the temperature rise 
during superheating at pressure pis D = _ — . The ordin- 



ates of the Q-curve are T = T^ -\- D, and the abscissas are 



A(/)s = A4>,a + Cp loge 



T, + D 



(138) 



in which Tv, D and Cp are known and A^^a can be obtained 
from the tables. _ 

A difficulty arises in selecting the proper value of Cp, because 
the mean specific heat is dependent on D, which is initially 
unknown. Hence it is necessary to adopt the " cut and try 
method." That is, a trial _value of Cp is assumed and D is com- 
puted; then the value of Cp corresponding to the pressure and 
to D is obtained from the curves, and if it is the same as the 
trial value the assumption was correct; but if there is much 
difference, a new value must be assumed and the process must 
be repeated. 



Constant -Pressure Curves, or P-curves. 

(h) For saturated steam the P-curves are isothermals; for 
superheated steam they are not. In the latter case, the rela- 
tion between A^j and (r„ + D), the temperature after super- 
Jieating, is given by the Eq. (138). If this is solved for any 



PROPERTIES OF STEAM 



143 



fixed pressure, Tv and A^^a become constants, and the variables 
are A^^ and {T^ + D) with related values of Cj,. Correspond- 
ing values of these variables would be used in plotting the 
P-curves, several of which are shown in Fig. 44. 

The temperature of saturation T^ for any pressure can be 
found by using these curves, for it is given by the ordinate of 
the point of intersection between the corresponding P-curve and 
the Saturation Curve. 

The Final T<|)-chart. 

(i) The final T<^-chart, Plate I in the Appendix,* contains all 
the curves described in this section, and to it has been added a 
scale for the absolute pressures corresponding to the tempera- 
tures of saturation. 

For a point anywhere on it in the Saturation Region there can 
be read directly the corresponding values of r„, A^^, x, V, p, 
and AQ. The latter is given either by the Q-curve or by area; 
the values of q and xr are given by areas; and the pressures can 
be read either on the scale at the left or by extending the isother- 
mal to intersect the S-curve, thus finding the corresponding 
P-curve in the superheated region. 

If the point is on the W-curve, T^, A(t>i, and p can be read 
directly, while g is given by the area below the curve. 

For a point on the saturation line the values of T^, A^^a, X, V, 
and p can be read at once. 

If the point is in the Region of Superheat, T, Acjtg, A(j>sa, p, and 
AQ can be read directly; the increase in temperature above 
saturation is D = T — Tv', the B.t.u. superheat, AQ^, is given 
either by an area, or by (AQ — X) ; and the entropy of super- 
heat A(f)^ is {A(t)s — A0sa)- 

If any expansion line is drawn on the chart, all of the above- 
mentioned quantities can be read for each point on the line. If 
the lines inclosing a cycle are drawn, the work done per cycle is 
of course given by the area surrounded. 

It is important to note that the quantities given by the 
Q-curves are values of (xr + q) , not (xp -f- q) , and contain the 
external work of vaporization (xA Pu) . 

* A larger and more accurate T</)-chart is contained in Peabody's Steam and 
Entropy Tables, published by Wiley & Sons. 



144 



HEAT-POWER ENGINEERING 



82. The MoUier Chart, or Q<^-Chart. (a) This chart, Fig. 45, is 
constructed with Q^-coordinates. On it are drawn lines for 
constant pressure (P-curves) ; for constant quahties (X-curves) 




1«JU 1300 1200 1100 1000 900 

Fig. 45. — Mollier or Heat-Entropy Chart. 

for wet steam; and for constant temperatures (T-curves) for 
superheated steam. The boundary Hne between the Regions of 
Saturation and Superheat is the Saturation Line (S-curve). 

(b) For wet steam AQx = xr -}- q and A^^ = A0z + xAcpv 
If the pressure is constant, x, AQx, and A^^ are the only variables. 
Then by substituting different qualities, related values of AQx 
and A0X may be found and these can be used in plotting the 
P-curve. A series of such curves is shown in the figure. 

(c) Lines joining points of the same quality on the different 
P-curves constitute the X-curves. 

(d) For superheated steam 

AQs = \ + CpD and A0. = A0,a + Cp log^ "^^ ^ ^ • 

If the pressure is constant, AQs, A0s, and (T^ -{- D) are the 
variables. By substituting different values of D in these 
equations, the AQs and A^s coordinates of points on the P-curve 
may be found. 

(e) Lines through points of like temperatures are the T-curves, 
and as drawn these give the temperatures in degrees Fahr., not 
absolute. Lines through points representing the same increase 
of temperatures above saturation constitute D-curves. 

(f) The final Q<^-chart is given in Plate II in the Appendix. 
This has all the curves just discussed, except the D-curves. 



PROPERTIES OF STEAM 145 

For any point on it there can be read at once the values of 
AQ, A(f), p, and x (or t). The chart is of particular advantage in 
solving problems involving reversible adiabatic expansion, for it 
shows at once the changes in AQ, in pressure and in quality (or 
in temperature of superheat) during such a process. It should 
be noted, however, that AQ = xr -\- q, — not xp + g, — and thus 
contains the external work of vaporization (xA Pu) . 

If any expansion line is drawn on this chart, the state of the 
material at each point on the line can be quickly determined. 



CHAPTER XI. 

VOLUME CHANGES OF VAPORS. 

83. General. Saturated and superheated vapors, like gases, 
may be made to change volume in many different ways, but the 
general study of such transformations may be based on a few- 
simple cases. The laws governing these changes are different 
from those for similar gas processes, and this is because of the 
different properties of the materials dealt with. For conven- 
ience the order of treatment in this chapter is different from 
that of Chapter V. 

84. Constant-Pressure and Isothermal Volume-Changes for 
Saturated Vapors, (a) Fixing the pressure of a saturated 
vapor, wet or dry, fixes the temperature; hence a constant- 
pressure change of such material must also be a constant-tem- 
perature, or isothermal one. 

The line ah in the FV-diagram, Fig. 46, and in the T<^-diagram, 
Fig. 47, is the graph of an isobaric or isothermal change for dry 
saturated vapor. In Fig. 46, the abscissa of point a represents 
the volume of unit weight of the liquid at the temperature of 
vaporization corresponding to the pressure Pi. By the addi- 
tion of heat the liquid can be vaporized to any desired extent 
until finally it has all become dry saturated vapor. This is an 
expansion at constant pressure and at constant temperature and 
is the only isothermal expansion possible with saturated vapor. 
It follows that isobaric and isothermal volume changes of satu- 
rated vapors can only occur during vaporization or condensa- 
tion of the material. This is equivalent to saying that such 
transformations are always accompanied by quaUty changes. 

Such volume changes cannot be carried beyond a quality of 
100 per cent, because then the material will all be saturated 
steam, with the specific volume corresponding to the existing 
pressure, and because further addition of heat at constant pres- 
sure must increase the volume of unit weight above the value at 
saturation, hence must superheat the vapor. 

146 



VOLUME CHANGES OF VAPORS 



[47 



Equation for Isobaric and Isothermal Changes of Saturated 
Vapors. 

(b) The equation of such changes in terms of P and V must 
be the same as that for the constant-pressure change of gases; 
that is, 

p 70 = p = Constant. 

There is, however, a real difference in the two cases. When 
dealing with gases it is possible, in imagination at least, to carry 
the isobaric expansion to any desired volume, while in the case 




Volume 

Fig. 46. — PV-Diagram for Vapor. 

of saturated vapors expansion per pound cannot be carried be- 
yond the specific volume corresponding to the existing pressure 
without changing the nature of the material and its behavior. 

The volume occupied by one pound of the material depends on 
the quality x, and can be computed from 

V = 0.017 -[■ xu = xV (approx.). 

This is, of course, true, no matter what process the material has 
undergone, and applies in all cases that follow. 

Heat Changes during Isobaric or Isothermal Changes of Satu- 
rated Vapors. 

(c) If the expansion starts with all the material as liquid at 
the temperature of vaporization, that is, with an initial vapor 
volume equal to zero, the heat change is merely that accompany- 



148 



HEAT- POWER ENGINEERING 



ing vaporization, and must equal the latent heat of vaporiza- 
tion per pound of material if the condition of dry saturation is 
reached. Hence the heat added is 



AQ = r = (p-\-APti), 



(139) 



where u is the volume change represented by the distance ab 
in Fig. 46 and AQ is the area below ab in Fig. 47. In the case 
of water vapor, the values of all the quantities occurring in this 
equation may be obtained from the Steam Table given in the 
Appendix.* 

If the pound of material is not completely vaporized but has 
a quality equal to x, then 

AQ = xr = xp -}- xAPu, .... (140) 

in which xu is the volume change, which is shown by the distance 
ab' in Fig. 46 and AQ is the area below ab\ in Fig. 47. 




Entropy Change A ^ 

Fig. 47. — T0-Diagram for Vapor. 



If the expansion is from quality xi to X2, with corresponding 
volume change from xiu to X2U (not shown in the figure), the 
case is general, and the change in associated heat is 

AQ = xiY — X\r 

= (X2 - xi) (p + AFu) a (141) 

* For steam, m = (V — 0.017 ±), in which V may be obtained from the Steam 
Tables. 



VOLUME CHANGES OF VAPORS 1 49 

Work during Isobaric or Isothermal Changes of Saturated 
Vapors. 

(d) The External Latent Heat of vaporization is that part of 
the total heat which does the external work accompanying the 
increase of volume; it must therefore be equivalent to the ex- 
ternal work done. Hence in vaporizing to quality x, per pound 
of material, 

A£ = x-^Pm B.t.u (142) 

and 

778 ^E^X'Pu ft.-lbs (143) 

This work is shown in Fig. 46 by the area below ah' . For the 
case in which x = i.oo, it is the area below ah. 

With change of quality from Xi to Xi the work done is, 

AE = (X2-X1) APu B.t.u. . . . (144) 
and 

778 A£ = (x2 - Xi) Pz^ ft.-lbs (145) 

85. Constant-Pressure Volume Changes of Superheated 
Vapors, (a) Starting from the point h in Figs. 46 and 47, the 
dry and saturated vapor may be made to still further expand at 
constant pressure to some point Ci by superheating, that is, by 
raising the temperature above that corresponding to saturation 
at that pressure. The further this expansion continues the 
more nearly the behavior resembles that of a gas, and there is 
no theoretical limit to such expansion, as there was in the case of 
the saturated vapor. 

Equation of Isobaric Change of Superheated Vapor. 

(b) The equation in terms of P and V must be the same as 
that already developed for gases and saturated vapors, namely, 

p 70 = p = Constant. 

Heat Change during Isobaric Changes of Superheated Vapor. 

(c) As the temperature must be raised at constant pressure 
in order to increase the volume, or lowered at constant pressure 
to reduce the volume, it follows that a quantity of heat equal 
to the specific heat at constant pressure, C^, must be added 
or abstracted per degree change. Then for heat added ahove 
saturation ^^ 

AQd= J CpdT, 



150 HEAT-POWER ENGINEERING 

or, using the mean specific heat Cp for the temperature range D 
measured from the temperature of saturation, 

AQd= CpD (146) 

In Fig. 47 this is shown by the area below bci for a case in which 
the heat change is reversible. 

For an isobaric change from superheat temperature Di to D2 

AQ = (CpD)2 - (C^D), (147) 

This is equivalent to AQ = C'p {Di — Di) = C'p {T2 — Ti), where 
Cp is the mean specific heat for the temperature range involved. 
In Fig. 47 this heat change is shown for reversible conditions by 
the area below C1C2. 

The foregoing equations giving the heat change are not 
sufficient for use in engineering problems as they generally 
occur. It is usually not only necessary to know the range of 
superheat, but also the volume change accompanying it. In 
the case of gases, this can be found from the Law of Charles, 
but superheated vapors as generally treated in engineering are 
not far enough removed from the condition of saturation to even 
sensibly obey that law. 

It is possible to find this volume change for superheated 
water vapor by using the approximate equation of Tumlirz pre- 
viously given as Eq. (134). Writing this for volumes Vi and V2 
and then dividing gives, for pressures in pounds per square inch,, 

Vi ^ Ti - 0.4293 p, 

V2 T2- 04293 p2 ^^^ 

Since p2 = pi during an isobaric change, this equation reduces 
to the form 

Vi Ti — Constant 



V2 T2 — Constant' 



(149) 



in which the constant has a different value for every pressure. 

The effect of this corrective constant becomes less with in- 
crease of temperature or decrease of pressure, and there is an 
accompanying closer approach of the equation to that of Charles' 
Law and a closer resemblance of the superheated vapor to an 
ideal gas. 



VOLUME CHANGES OF VAPORS 151 

Work during Isobaric Changes of Superheated Vapor. 

(d) During an isobaric change with one pound of any work- 
ing material the work is 

778 ^E = P (V2 - Vi) ft.-lbs., . . . (150) 

which was first developed in the case of gases as Eq. (24). If, in 
Fig. 46, the expansion is from C\ to C2, the work done is given 
by the area below Cic^. 

86. Isothermal-Volume Changes of Superheated Vapors. 

(a) These must in a general way resemble the isothermal 
changes of gases, since superheated vapors approximate the 
gaseous conditions. The exact behavior of any particular vapor 
under these conditions must, however, be determined by experi- 
ment. For superheated water vapor the necessary information 
can be obtained from the approximate equation of Tumlirz, 

Equation of Isothermal Change of Superheated Water Vapor. 

' (b) Rearranging the Tumlirz equation (134) and maintaining 
T constant gives the following for isothermal changes for this 
material, for p in pounds per square inch, 

pY + 0.256^ = 0.5962 T = Constant, . . (151) 
and from Eq. (135), for P in pounds per square /oo^ 

PV + 0.256 P = 85.86 T = Constant. . . (152) 
Comparing this latter with the Eq. (14) for gases, namely, 
PV = RT, 
it is evident that it differs only in the addition of a second 
term (0.256 P) in the first member. Obviously the smaller the 
numerical value of the pressure the smaller will be this cor- 
rective factor and the more nearly will the vapor obey the ideal 
gas law. If Eqs. (151) and (152) be divided by T, it becomes 
apparent that the greater the numerical value of T the smaller 
will be the effect of the corrective factor and therefore the more 
nearly will the material approach the condition of an ideal gas. 

Work during Isothermal Changes of Superheated Vapor. 

(c) The work done by an expanding vapor, as well as gas, is 
given in all cases by the expression first developed as Eq. (41), 

778 A£ = r^'Pf^F ft.-lbs. 

tJVi 



152 HEAT-POWER ENGINEERING 

However, in order to perform the integration in any case, it is 
necessary to know the relation between P and V, and this is a 
matter for experimental determination. The relation given by 
the equation of Tumlirz, Eq. (135), may be used for superheated 
water vapor. From this equation, 

p^ 85-86 r 
V + 0.256' 

which value may be substituted in the type integral, and the 
integration performed, giving per pound of water vapor 

778 A£ = 85.86 r/^_^^^^^ 

= 85.86 nog 4^ + ^;g ft.-ibs. (153) 

Eq. (43b), for work during isothermal changes of gases, may be 
written 

V2 



778 AE = [P,Y,\ogeYj= ^^^°g«Vi 

Comparing Eq, (153) with;this, it again appears that the higher 
the temperature and the lower the pressure the more nearly do 
the equations developed for superheated water vapor approach 
those for the behavior of gases, and by analogy the same must 
be true of the behavior of all superheated vapors. 

If, in Fig. 46, the isothermal expansion is from ci to d, the 
work is represented by the area below C2d. 

Heat Change during Isothermal Changes of Superheated Vapors. 

(d) Applying Eq. (i), 

A(2 = A5 + A/ + AE, 

to this case, it is evident that the term A^ must be zero, since 
temperature does not change; but A/ must have some value 
other than zero, since the materials cannot be said to even 
sensibly approach the condition of ideal gases. The term AE 
must also have a valufe other than zero if work is to be done by 
or upon the superheated vapor. For any case AE can be readily 
found, but A/ is more difficult to evaluate, and any equation for 
the value of LQ which could be developed would necessarily be 
a very cumbersome one. 



VOLUME CHANGES OF VAPORS 1 53 

(e) Fortunately the T(^-diagram offers a simple means of deter- 
mining AQ, since this quantity is represented by an area on that 
diagram, when the change is reversible. 

Assume for instance that it is desired to find the heat required 
when one pound of water vapor is expanded isothermally and 
reversibly from a pressure Pi and a temperature T2 above satu- 
ration temperature Tv^, to a lower pressure P3. It is only 
necessary to draw the horizontal line C2d in Fig. 47, between the 
two pressure lines and at the desired temperature, and then 
determine the area under c^d. 

Fig. 47 is only a special case of Plate I of the Appendix, and 
in practice the latter would be used. 

(f) It should be noted that the Mollier Chart can not be used 
for finding AQ for an isothermal process in the superheated 
region. The heat quantities plotted on the chart are those used 
to take the material at constant pressure from 32° F. to the con- 
ditions shown. In the saturated region constant-pressure con- 
ditions are isothermal, so that isothermal heat changes can be 
determined. In the superheated region this is not true. 

87. Adiabatic Changes of Saturated Vapors, (a) With the 
exception of problems involving the flow of vapors in which the 
material is accelerated as a whole, the adiabatic changes of vapors 
which are considered by the engineer are thermodynamically 
reversible in the ideal case. In the following paragraphs only 
these reversible processes will be considered, leaving the more 
complicated irreversible processes for later development. 

Since reversible adiabatic changes are also isentropic ones, 
their graph on the T0-diagram must be a vertical line. This 
offers a very easy means of studying these changes in every case 
where there are sufficient experimental data for the drawing of 
this diagram. 

(b) The diagram in Fig. 48 is developed from the T</)-dia- 
gram for water vapor with the lines of constant quality shown — 
originally given in Fig. 42 (a) and Plate I. To this have been 
added vertical lines representing reversible adiabatic expansions 
starting at each 20 per cent of quality at the pressure Pi. The 
diagram shows that when the initial quality is high (point a in 
Fig. 48) the quality of water vapor must decrease as the expansion 
progresses, and when the initial quality is low (point b) it must in- 



154 



HEAT-POWER ENGINEERING 



crease during expansion. Near the middle of the diagram, that 
is, with initial quality near 50 per cent, x remains nearly con- 



20/. 40 9« 60 $4 80 ?« 100^ Quality 




Entropy 
Fig: 48. — T</)-Diagram for Water Vapor. 

stant during the entire expansion. This is not necessarily a 
property of all vapors, as it depends on the relation between the 
various heat quantities and is thus a matter for experimental 
determination. 

This is well shown by considering the case of Ether Vapor. 
The T0-diagram for this material is given in Fig. 49. As in the 







D5«2 


H 4054 6 


Qfi 


05^1 


0054 


Ether 




/ 






1/ 
1/ 




i/ 
/ / 






L 


1 


a/ 
3/ 

1 




'I 


m 


/ 

60? 


^ / 

80^ 


K 


)Ofc 


i 



Entropy 
Fig. 49.- 



•T0-Diagram for Ether Vapor. 



last case, the constant-quality lines and isentropic lines for every 
20 per cent initial quality are drawn. It is evident from the 
figure that during reversible adiabatic expansion of ether vapor 



VOLUME CHANGES OF VAPORS 155 

the quality must continually increase, whatever its initial value 
may be. 

(c) At any initial quality between o per cent and 100 per cent 
the quality changes will be governed by the relative quantities of 
liquid and vapor present, as can be seen for the case of water by 
referring to Fig. 48. In this case large quantities of liquid make 
available so much heat with decrease of pressure or temperature 
that evaporation (or "quality increase") must occur as expansion 
progresses; large quantities of vapor make available so small a quan- 
tity of heat by pressure drop alone that condensation must occur. 

With initial qualities of about 50 per cent, the two efifects 
approximately balance and the quality remains almost constant. 

(d) The case of ether as already shown is very different. 
Referring to Fig. 49, it is seen that with expansion starting at 
any quality between o per cent and 100 per cent the heat liber- 
ated due to pressure drop alone is more than sufficient to do the 
necessary external work, and the expanding material must ab- 
sorb part of the liberated heat. When the quality is less than 
100 per cent, this is done by vaporization, with possible super- 
heating toward the end of the process; and when the quality 
is equal to or greater than 100 per cent, superheating occurs 
throughout the expansion. 

Comparison of Figs. 48 and 49 shows that because the heat 
of the liquid varies much more rapidly and is much greater in 
quantity in the case of ether vapor, the quality lines for that 
vapor all slope in the same direction, thus accounting for the 
difference in phenomena occurring during adiabatic expansion. 

Equation of Reversible Adiabatic Changes of Saturated Vapors. 

(e) Since these changes are generally studied by means of the 
T0-diagram, the most useful equation is 

A<?!) = Constant, or (A(/)x)i = (A0x)2. 

This equation gives no direct means of plotting the curves rep- 
resenting adiabatic expansion to PV-coordinates, but may be 
used indirectly for that purpose. 

First, the quality at the end of adiabatic expansion, from 
pressure pi and quality Xi to pressure p2, may be computed by 
solving for xt in the following equation : 

(A0i -F X A0,,)i = (A(/)z + X A0O2. . ... (154) 



156 HEAT-POWER ENGINEERING 

Then, the volume occupied by unit weight of the substance,, 
at the end of the expansion, is found by multiplying the specific 
volume by X2. 

As already shown, the isentropic line corresponding to Eq. 154 
gives a means of reading directly the quality of the expanding 
material on either the T0-diagram or the Mollier Chart. 

(f ) For water vapor at common operating pressures and with 
initial quality between 100 and 70 per cent, the relations be- 
tween pressure and volume during adiabatic expansion are given 
approximately, but very accurately, by the equation 

P F" = Constant, (155) 

in which the value of n is given by the following equation, 

n = 1.035 +o.i:\:, (156) 

where x is the initial quality expressed as a decimal fraction. 

The PV relations can also be obtained directly from the 
T<^-chart. 

Work Done during Adiabatic Changes of Saturated Vapors. 

(g) Since all the work done during such an expansion must 
be obtained at the expense of intrinsic heat energy, and since 
no heat energy is used for other purposes, it follows that 
if {xr -\- q — xAPu)i = (xp + 2)1 represent the intrinsic heat 
energy before an adiabatic change and (xr + g — xAPu)2 = 
(xp + 2)2, the intrinsic heat energy after such a change, the 
External Work Done is 

AE = (xr + q — xAPu)i — (xr -\- q — xAPu)^ . (157) 
";= (xipi + 2i) - (x2P2 + 22) (158) 

In using this equation the initial conditions are known : xi is 
obtained from Eq. 154, and p2 and qi are found from the Vapor 
Tables for pressure p2. 

(h) If the PV-diagram, Fig, 50, be for one pound of steam, 
then when the point h is reached the heat-energy (xAPu)i has been 
abstracted from the steam and absorbed by displacing a piston 
or surrounding media against resistance. Thus there remain 
(xp + 2)1 heat units with which to begin the adiabatic expan- 
sion. At point c, there are (xp + 2)2 heat units left in the 
steam, and the quantity (xAPu)^ would not appear unless either 
by compression or some equivalent process the volume of the 



VOLUME CHANGES OF VAPORS 



157 



steam is contracted isobarically an amount X2W2 to the volume of 
the hquid, as shown at d. 

The area below ab is {xAPu)i B.t.u.; the area below be shows 
the work done, or heat utilized during adiabatic expansion alone, 




Volumes 
Fig, 50. — PV-Diagrara. 



Entropy 

Fig. 51. — T(/)-Diagram. 



and is [(xp]-{- q)i — (xp + 3)2] B.t.u. ; the area below cd is {xAPu)^ 
B.t.u. 

(i) On the T</)-diagram, Fig. 51, the areas below lines such as 
oab represent {xr + g) quantities which include the external 
latent heat of vaporization. From these quantities must be de- 
ducted the appropriate values of xAPu to obtain the heat in the 
steam during an isentropic process. (Note that in the T0-chart, 
Plate I, the xAPu quantities are also included in the values 
given by the Q-curves.) 

(j) On the Mollier diagram the abscissas (AQ) also include 
the external work, and this latter must be deducted when con- 
sidering the heat utilized during adiabatic expansion alone (see 
(g) above). 

88. Adiabatic Changes of Superheated Vapors, (a) These 
changes, like those for saturated vapors, are best studied by 
means of the T^-diagram. Vertical lines, such as that through 
e in Fig. 48, drawn to represent reversible adiabatic expansion of 
superheated water vapor, show that as the expansion is carried 
to lower pressures the material approaches the saturated con- 
dition and may indeed attain a quality less than unity. On the 
other hand, similar lines on the T0-diagram for ether, Fig. 49, 
show that if such an expansion starts with superheated vapor the 
superheat increases as the expansion continues. 



158 HEAT-POWER ENGINEERING 

Equation of Reversible Adiabatic Changes of Superheated 
Vapors. 

(b) As in the case of saturated vapors, the general equation 
for reversible adiabatic changes of superheated vapor is 

A0 = Constant, or (A0s)i = (A<^)2. 

If the steam is expanded to wetness, the quality may be found 
by solving for X2 in the following equation: 

(A0«)i = (A0Z + xA4>,), (159) 

{A4>s)i can be computed from Eq. 138, (A0i)2 and (A0t,)2, in the 
case of water vapor, can be obtained directly from the Steam 
Tables. 

If the expansion takes place entirely in the Region of Super- 
heat, the final temperature T2 = (T^ -\- D)^ can be found from 

/ - T^-[- D\ 

(A0s)i = (A</)sa + Cploge — y. — )• . . (160) 

Here Cp is the mean specific heat for the temperature range 
D2 = (T — Ty)2 and T^^ is the temperature of vaporization at 
the terminal pressure. 

External Work Done during Adiabatic Changes of Superheated 
Vapors. 

(c) As in other cases of adiabatic changes, the external work 
done during this reversible adiabatic change is equal to the 
intrinsic heat change. During a constant-pressure change from 
liquid at the temperature of vaporization to superheated vapor, 
the external work per pound is 

AEp = AP(Ys - 0.017) B.t.u., . . . (161) 

where Vg is the specific volume of the superheated steam from 
Eq. (134) ; hence the external work done, if the steam remains in 
the superheated state throughout the isentropic expansion, is 

AE, = \-\- J^CpdT- AEJ -W-h J^CpdT-AEpl (162) 

= [X + CpD-AEp\y -[X + ClD -AEp]2 (163) 

in which A is found from Eq. (160) 



VOLUME CHANGES OF VAPORS 1 59 

If vapor initially superheated is expanded to wetness with 
quality X2, the external work done is 

AE,, = [X + CpD - AEp]i - [xp + q]2, . . . (164) 

in which X2 is found from Eq. (159). 

On the PV-diagram this work is represented by the area below 
the expansion line. In using either the T^-diagram or the 
Mollier diagram to obtain the work done during isentropic 
expansion alone, it is necessary to deduct the AEp quantities 
(and the APu quantities if entering the saturation region) from 
the heat values found. 

89. Constant-Volume Changes of Saturated Vapors, (a) If 

a saturated vapor is to change pressure at constant volume, there 
must be a quality change, because the same weight of material 
in the form of vapor cannot occupy a given space at two differ- 
ent temperatures. During a pressure drop there is a tendency 
for saturated vapor to increase in volume, hence if the volume 
is maintained constant there must be a decrease of quality ; that 
is, condensation must take place. The reverse is of course true 
for a pressure rise. 

Equation of Constant-Volume Change of Saturated Vapor. 

(b) As in previous cases, the equation of a constant-volume 
change is, in terms of pressure and volume, 

V = Constant. 

Heat Change during Constant- Volume Change of Saturated 
Vapor. 

(c) It was shown in Section 70 that the quality of saturated 
vapor could be found by dividing the volume occupied per pound 
of mixed vapor and liquid by the specific volume corresponding to 
the pressure existing. By using this method the quality changes 
which occur during a constant- volume change of saturated vapor 
may be found, and when the quality at any pressure is known 
the heat associated with the vapor may be determined. 

90. Constant-Volume Changes of Superheated Vapors. 

(a) When a superheated vapor changes pressure at a constant 
volume, there must be a temperature change similar, but not 
equal, to that occurring in the case of an ideal gas undergoing 



l6o HEAT-POWER ENGINEERING 

the same sort of change. The equation of Tumlirz, Eq. (134), 
may be used to find the temperature of water vapor correspond^ 
ing to any pressure and volume, and hence such changes (oi 
their equivalents, if irreversible) can be plotted to PV or T^ 
coordinates. 

Equation of Constant- Volume Changes of Superheated Vapors. 

(b) As in all other cases, the equation in terms of PV coordi^ 
nates is 

V = Constant. 

Heat Change during Constant-Volume Change of Superheated 
Vapor. 

(c) Since the temperature and pressure can be found for any 
point in a constant-volume pressure change of superheated 
vapor, the total associated heat can also be found for every 
point. The difference between the total at beginning and end 
of the pressure change must be the change of associated heat. 



CHAPTER XII. 

VAPOR CYCLES. 

91. Carnot Cycle with Dry Saturated Steam, (a) The Carnot 
cycle may be carried out with a saturated vapor of any kind in 
the same apparatus as was assumed in Section 49 and shown 
in Fig. 17. For simphcity assume the cylinder to contain unit 
weight of water at the temperature Ti. Then the volume occu- 
pied by the liquid, inclosed by the cyhnder head, cylinder walls, 
and piston, will be that of unit weight of water at temperature 
Ti and corresponding pressure. This is plotted as the point a 
on the PV-diagram, in Fig, 52, with volume greatly exaggerated. 

If heat is added to the liquid from the hot body U and 
the piston is allowed to move out at just the proper rate 
to maintain a constant pressure on the working substance, 
vaporization will occur at constant pressure and therefore at 
constant temperature. The volume would consequently in- 
crease isothermally, or the process would be an isothermal ex- 
pansion. 

When vaporization is complete the volume attained will be 
the specific volume, Vs, of water vapor at temperature Ti and 
corresponding pressure. The isothermal expansion will then be 
represented by the constant pressure line ah. 

If now the nonconducting cylinder cover Z is applied and the 
piston allowed to continue its outward motion, the expansion of 
the vapor must be adiabatic. The actual shape of the line 
representing such expansion will be given approximately by 
P F" = Constant, and is represented by the curve be, on which, 
c is a point where the temperature has reached that of the cold 
body, T2. 

If now Z is replaced by the cold body and the piston is forced 
inward, condensation must occur, the heat liberated being ab- 
sorbed by the cold body. Condensation, like evaporation, is a 
change at constant temperature and constant pressure, and hence 
is represented by a horizontal line from c toward the left. 

161 



l62 



HEAT-POWER ENGINEERING 



To complete a Carnot cycle, it is necessary to stop the process 
of condensation when the volume has decreased to some value 
Vd, so chosen that the final adiabatic compression will bring the 
material back to the liquid form with conditions Ti, Pa, and Fo. 



a h 














\ 














\ 


\ 

\ 














^'l 


%. 


Car 


lot 






1 




•Po, 








\ 




^ 




^^^^^ 






> 








"--—-_ 


""] 


^ 










°c 



Volumes 
Fig. 52. — PV-Diagram for Carnot Cycle with Dry Saturated Water Vapor at b. 

(b) The T0-diagram of the cycle is drawn in Fig. 53, on which 
the water curve and saturation curve are indicated by dotted lines. 
This diagram is lettered to correspond with Fig. 52. It shows 
how the quality of the steam must decrease during the adiabatic 
expansion be, and how by stopping the condensation, or iso- 
thermal compression, at the proper point, d, it is possible to 
return the material to the liquid condition at temperature Ti by 
adiabatic compression da. 

Note that the T^-diagrams for the Carnot cycle for vapor and 
gas are identical, but that this is not true for the PV-diagrams 
because of the difference in the properties of the materials. 



Work per Pound of Dry Saturated Water Vapor Operating in 
Carnot Cycle. 

(c) The work done per cycle can be obtained in several ways, 
two of which will be considered. They are practically the same 
as those previously used for gas cycles. 

(d) The first method is to take the algebraic sum of the quan- 
tities of work done during the several processes of the cycle. 



VAPOR CYCLES 



163 



(i) The work during the isothermal expansion equals — g (¥& — Va) 

B.t.u., and (2) that during the isothermal compression similarly 

equals -^ (Vc - Va) B.t.u. (3) The work during adiabatic ex- 

775 
pansion must be, as shown in Eq. (158), the difference between 
the quantities of intrinsic heat energy above 32° F. at the be- 
ginning and end of the process; that is, (gs + Pb) — (2c + oCcPc)- 
(4) Similarly, the work during adiabatic compression is 
Qa - (qd + Xdpd)' The values of the qualities Xc and Xd can be 
found from the constant-entropy equation (154) or from either 









a 




TX 






h 






















/ 












1 








1' 




Car 


not 






f6 




e 




1 






T2 






\ 


% 










>. 


^ 





































Fig. 53- 



Entropy Changes 
• T(^-Diagram for Camot Cycle with Dry Saturated Water Vapor at h. 



of the entropy diagrams ; hence in any problem all the terms are 
known and the total work done during the cycle equals the 
algebraic sum of the four expressions. 

(e) The second method and more direct one is to subtract 
from the total heat supplied the total heat rejected; the differ- 
ence must be the heat converted into work, and must be rep- 
resented by the area within the four lines of the cycle. 

The heat supplied during the isothermal expansion is n, the 
latent heat of vaporization of the material at the temperature 
Ti. The heat rejected is the part of the latent heat liberated 
during the partial condensation and is {xji — Xdr2) = ^2 {xc — Xd) , 
in which Xc and Xd are determined from the constant-entropy 
equation* (154) or from either of the entropy diagrams. The 

* Just as Xc is the quality at the end of adiabatic expansion be, so xa may be 
considered as the quality at the end of an adiabatic expansion ad. The constant- 
entropy equation is applied to the line he to find Xc and to the line ad to find xd- 



1 64 HEAT-POWER ENGINEERING 

external work done must then be, when the steam is dry and 
saturated at the beginning of expansion, 

AE = A(2i - AG = rx-r2 (x. - Xi) B.t.u. . . (165) 
and 

778 ^E = 778 [r, - 7-2 {xc - Xd)] ft.-lbs (166) 

The expression numbered (165) is really obvious from the 
T0-diagram drawn in Fig. 53. 

(f) From Fig. 53 it is also seen that 

A£= (Ti- r2)A0„ = (ri- 7^2)^. . . (167) 

The last form is the simpler in use. In it the expression 

— ^=1 — — is the efficiency Ef^ of the cycle, as will be shown 
1 1 

next, hence 

AE = riXEfc (168) 



Efficiency of the Carnot Cycle Using Dry Saturated Water 
Vapor as a Working Substance. 

(g) The efficiency must of course equal the ratio of the work 
done per cycle to the heat supplied per cycle; hence from Eq. 
(165) 

T^r r i — f2 (Xc — Xd) 

A more convenient expression can be found directly from the 
T0-diagram. 

(h) Remembering that area under the line ab in Fig. 53 repre- 
sents heat supplied from the hot body, and that the area of the 
cycle represents heat converted into work, it is evident that 

77f ri (A<^, - A4>a) ~ T, {A<t>c - A0,) ri- T, 

^^' ^ r, (A0, - A0„) = —Tr~' ' ^'^^^ 

which is the same as the expression for efficiency of the Carnot 
engine using gas as a working substance. 

(i) The Carnot cycle, consisting as it does of two reversible 
isothermals crossed by two reversible adiabatics, must have 
identical T0-diagrams for all working substances. Since the 
development just given depends only on this diagram and not 



VAPOR CYCLES 



165 



upon the properties of the material, it follows that the expression 



T, 



must give the efficiency of the Carnot cycle operating 



with any working substance. 

92. The Carnot Cycle with Any Vapor, (a) The case just con- 
sidered, in which the working vapor is brought to the dry satu- 
rated condition before adiabatic expansion begins, is the simplest 
possible case as far as the expressions for heat and work are con- 
cerned. But adiabatic expansion might begin with the liquid 
only partly vaporized by isothermal expansion; that is, with a 
quality, Xb, at the top of the adiabatic. Or, the vapor might be 
superheated before adiabatic expansion begins. Further, a mate- 
rial like ether, with properties markedly different from steam, and 
with different behavior during adiabatic expansion, might be used. 

In any case T —T 



and 



Efc 
AE 



T, 



(170) 



AQiXEf,, (171) 

where A^i is the heat added at constant temperature Ti to the 

liquid previously raised to that temperature. 

For steam initially dry and saturated, AQi = ri . . . (172) 

For steam initially wet, AQi = Xin . . (173) 







1 




Ti 






/ 




i 


T,S 


\/^ 




/ 








\ 












Carnot 


\ 






/ 








\ 






/ d 
1 

1 






To 






t 












g 








^C-At^ 


<A0> 




B 















Entropies 
[Fig. 54. — T<^-Diagram for Carnot Cycle with Superheated Steam. 

(b) For steam at pressure P, Fig. 54, superheated to temper- 
ature Ti, AQi is given by the area below ah. In the figure PP 



i66 



HEAT-POWER ENGINEERING 



is the constant-pressure curve through b and A^ga' is the entropy 
of saturation at this pressure. Evidently 

A(2i=ri + 7\(A03a'-A03„. + A0z)O (i74) 



= ri-l-ri 



(a4>J 



A<l>sa. + C,'\oge^^\ . (175) 



where the subscript 1 refers to the values corresponding to Ti 
and the primed quantities are those referring to the pressure at 
the point b: hence ri does not correspond to pressure P. 

(c) In Fig. 55 are shown PV- and T0-diagrams of Carnot 
cycles illustrating different possibilities when saturated and 




a 


hi 


-\6 


1 

1 






d 


T« ci 


^ 



(n^ Steam Wet at hi and 

V"'>' Dry at b 




r- 


T, 


■^■5?^ 


V 
'71 




% 




b 


/ 




Ti 


w 




' CI 






C Co 


Cl 



((t\ steam Superheated Through- 
out Expansion from 61 to Cl 



a 


f, 




\ 


"^^^^ 




To G 


Cl 



/ 

a 


1 


6 6, 


1 


;^ 


T2 


c 



(J-A Superheated Steam at 6] 
'' ^ ' Expanded to Wetness at C 






% I 


y 


'■/ 




y 


Ts fOx 


& 






f 



f^\ Ether Vapor- Dry at 6 becomes 

Superheated during Expansion 6c 



Fig- 55- — Carnot Cycles for Vapors — Various Possibilities. 



superheated vapor are used as working substances. The bold 
lines represent the isothermal reception and rejection of heat. 
In the PV-diagram these are horizontal only when the vapor is 
saturated. Figs. 55 (a), (b), and (c) are for steam, and in each 



VAPOR CYCLES 



167 



case abed is the diagram which is obtained with dry saturated 
vapor at b. Fig. 55 (d) is for ether. 

93. Clausius Cycle with Dry Saturated Water Vapor, (a) This 
cycle is often called the Rankine cycle, but as another cycle 
which is universally known by this latter name must also be 
considered, the name of Clausius will be used in this book to 
designate the cycle at present under consideration. As shown 
in the PV-diagram, Fig. 56, it consists of two constant-pressure 



? .^ 




























\ 


\. 














^ 




Claus 


us 








Y\ 


-G 












V 


^^- 


-..^ 














~~— — -. 







a 










cl 



Volumes 
Fig. 56. — PV-Diagram for Clausius Cycle with Dry Saturated Water Vapor at c. 

lines be and da joined by an adiabatic cd and what is practically 
a constant- volume line ab. The apparatus of Fig. 17 used in 
developing the Carnot cycle can also be used for the ideal 
Clausius cycle. 

The volume plotted at b is that of unit weight of water just 
ready to vaporize, corresponding to a of the Carnot cycle shown 
in Fig. 52. The addition of the latent heat of vaporization, ri, 
causes the material to expand at constant pressure until it 
occupies the specific volume Vc at c. This quantity of heat, as 
before, comes from the hot body at temperature Ti. 

The adiabatic expansion is exactly like that of the Carnot 
cycle and is produced in exactly the same way. 

The constant-pressure decrease of volume starts exactly like 
the similar line in the other cycle, but condensation is carried to 
completion by the removal of heat equal to Xdr2. The volume 



i68 



HEAT-POWER ENGINEERING 



Va is then the volume of unit weight of water at the temperature 
of vaporization corresponding to the lower pressure Pa. The 
heat given up during this condensation is received by the cold 
body at the constant temperature T2. 

The line ab which takes the place of the adiabatic compression 
of Carnot represents the heating of the liquid from temperature 
T2 to the higher value Ti, while the pressure rises from Pa to Pb. 
There will be a very small volume change in the liquid during this 
process, but it is so small in comparison with the other volume 
changes in the cycle that it may be neglected and the process 
considered as a constant-volume pressure rise. 

(b) The T^-diagram correspondingly lettered Is shown in Fig. 
57. The heat used to raise the temperature of the water must 





&, 










\ 




















/ 












\ 






/ 




Claus 


us 






\ 
\ 






,/ 












\ 
d 




/ 


r/i 


























\ 





















Entropies 
Fig- 57- — T(^-Diagram for Clausius Cycle with Dry Saturated Water Vapor at c. 



come from the hot body which has the temperature Ti, and during 
its reception the temperature of the water will vary from T^ to 
Tx. Hence the cycle does not fulfill the criterion for maximum 
efficiency because all heat is not received when the working sub- 
stance is at its highest temperature. It is also evident that the 
cycle is not reversible, because the addition of heat to the 
liquid exemplifies a process which is intrinsically irreversible. 
Strictly interpreted, the line ab in Fig. 57 represents a reversible 
process equivalent to the irreversible process ab of the Clausius 
cycle. 



VAPOR CYCLES 169 

Work per Pound of Water Vapor Carried through Clausius 

Cycle with Dry Saturated Vapor at Beginning of 

Adiabatic Expansion. 

(c) As before, AE = AQi — AQ2, from which the value of the 
work done per cycle may be determined. The heat AQi consists 
of two parts, (i) that added to raise the temperature of the water 
from T2 to Ti, and (2) the heat used in vaporizing during the 
volume change from Vb to Vc. The quantity AQ2 given up 
during the condensation, as already explained, can be determined 
as soon as the quality Xd is known. This is easily found from 
Eq. (154) or from either of the entropy diagrams. 

Then, 

AE^AQi-AQ2 = {(qb-qa) + ril-{xdrdlB.t.u. . (176) 
= Xi - 22 - Xdr2 (177) 

From inspection of the T0-diagram it is evident that the work 
done is given by the following expression, the symbol Cp standing 
for the mean specific heat of the liquid over the temperature 
range : 

AE=Cp{Ti- T2) + Ti (A0, - A06) 

- T2(Acl,d-A<^a). . . . . (178) 

Since (A^c — A(/)b) = A0„j, A^d = A(t)sa„ and A0„ = A(f)i^, Eq.(i78) 
may be written 

AE^\C^{Ti- T2)+T,A4>vA 

-{T2{A(j)sa,-A(l)Q} (179) 

A more useful formula, which may also be written from in- 
spection of the T0-diagram, is 

AE = ^{Tt-T2) + qi-q2-T2(Acl>i,-Acl>i;), . (180) 
J- 1 

all quantities in which may be obtained directly from the Steam 
Tables. 



170 HEAT-POWER ENGINEERING 

Efficiency of the Clausius Cycle with Dry Saturated Water 
Vapor at the Point c. 

(d) To find this item, it is only necessary to divide the work 
done, Eq. (177), by the heat supplied; then 

= 1-^.: (182) 

Ai — §2 

(e) This form is not readily comparable with the expression 
for the Carnot efficiency, and although the fact is already known 
that the Clausius efficiency must be lower than the other because 
of the addition of heat below maximum temperature, it is of 
interest to derive an expression which will show this difference. 
This can be done by using Eq. (178) in obtaining the efficiency 
expression, thus, 

^ . ^ AE ^ CATi- Ja) + Ti (A<t>c -A<f>,)- T2 (A y^ - A^g) 
A(2i CATi- T,) + Ti (A</,. - Ac/>6) 

= 1 - Tg (A</>, - A(Aa) . . 

CATi-T2) + TUAct>c-Acf>,) 

--il • • • (-4) 

The Carnot efficiency written in similar form is 

^/•=i-^=i-i- • • • • ('«5) 

In Eqs. (184) and (185), the magnitude of the last term deter- 
mines the value of the efficiency in each case, but inspection of 
the expressions as they stand does not show which of the last 
terms is the greater. If Fig. 57, which shows [the two cycles 
superposed, is consulted, the interpretation of the last terms is 
much simplified.* 

It is evident from the figure that the heat supplied during the 
Clausius cycle, equal to the area under abc, is greater than that 

* In the strict interpretation of Fig. 57, the hne ab is not the irreversible line 
of the Clausius cycle, but represents a reversible process which would give the 
same P, V, T conditions as the other, as mentioned before in connection with 
Fig. 57- 



VAPOR CYCLES 



171 



supplied during the Carnot cycle by the triangular area abdi, 
plus the area below adi. The heat rejected is, however, greater 
by the area below adi. Therefore in thecase of the Clausius cycle 
the heat rejected is increased in greater proportion than the heat 

received, and the fraction -^ for this cycle must be greater than 

for the Carnot, and hence the efficiency is less. 

94. The Clausius Cycle in General, (a) As in the case of the 
Carnot cycle, it is possible to imagine a Clausius cycle developed 



P b <; ! C 




b 


3l C 


1 


\ 

It 
1 \ 


a i 


iTd • 



/q\ steam Wet at C 1 and 

Dry at C 



P b C C 




Ch di 



\^d 



d d„\ 



((t\ steam Superheated Through- 
out Expansioa fromCl to rfl 




(^) Superheated Steam at Ci 
Expanded to Wetness at dl 




C^7) Ether Vaper- Dry at C Becomes 
Superheated During Expansion cd 



Fig. 58. — Clausius Cycles — •Various Possibilities. 

with the vapor of any material in either the saturated or super- 
heated condition. The general equations for the Clausius cycle 
will be given in the latter part of this section. Some of the 
possible cases are shown in Fig. 58, in which the heavy lines in 
all instances represent constant pressures. 

A word of explanation will probably help to make the con- 
struction of the diagrams in Fig. 58 clearer. In the Carnot cycle 
the upper and lower lines are defined as isothermals, while in the 



172 HEAT-POWER ENGINEERING 

Clausius cycle they are lines of constant pressure. For saturated 
vapors the two are the same, but for superheated vapors the two 
cycles present very different phenomena. The isobars give 
" horns " (at Ci) in the T^-diagrams when in the superheated 
region, the height of these being determined directly by the de- 
gree of superheat. 

(b) Another interesting difference results from the character- 
istics of this constant-pressure line. In the Clausius cycle the 
temperature rises during superheating, while in the Carnot it 
remains constant and the pressure drops. In the case of the 
former cycle, then, the hot body must have a temperature at least 
equal to that reached at the end of the superheating process and 
therefore higher than that of the working substance during the 
entire reception of heat. For this case, then, all the heat is 
received irreversibly. 

(c) It thus develops that for all Clausius cycles the heat re- 
ceived along the line ab is received irreversibly, the hot body 
having a temperature at least as high as Tc^, and for Clausius 
cycles in which superheating takes place, all the heat is received 
irreversibly, because the hot body must have a temperature at 
least as high as that attained by superheating. This cycle when 
using superheated vapor therefore departs still further from the 
criterion for maximum efficiency, and must have a theoretical 
efficiency lower than that of the same cycle with saturated vapor 
having the same maximum temperature. This conclusion is the 
more interesting because, notwithstanding the lower theoretical 
efficiency, real engines operating on this cycle obtain their highest 
commercial efficiency with superheated vapor. The reason for 
this will be brought out in a later chapter. 

(d) For the Clausius cycle with the adiabatic expansion start- 
ing with wet steam, with quality Xi, 

AE=^{T,- T,) +q,-q2-n {Acf^i, - A0;J, (186) 
J- 1 
and ^p 

Ef.^ -^ (187) 

Xiri+gi-22 

(e) In the general case the quality (or temperature of super- 
heat) at the end of the adiabatic expansion must first be found. 
This can be done by solving for Xd (or Dd) from 

iAct>i -f xA4>v + A0z>)<i = (A0Z + xAcf>, + A0,))„ . . (188) 



or, ( A<^j + :x;A0„ + Cp loge 



VAPOR CYCLES I 73 

r„ + m 



A<^; + xA(/>, + Cp loge ^' ^ ^ ) . . (189) 

If the steam is initially superheated Xc = 1 ; if wet, the entropy 
of superheat (A0z))c disappears. Should the value of Xa found 
be greater than i.oo, it indicates that the steam is still super- 
heated, then Dd should be determined, using xa = 1.* 

Having determined xa (or Dd), the work may then be found 
from _ _ 

AE = {g+xr + CpD)c - {q+xr + CpD)d. . (190) 

Also, the work may be found from 

AE =AQi-AQ2, (191) 

in which the values of AQi and AQ2, the heat supplied and the 
heat rejected, are equal respectively to the heat above 32° F., 
at the beginning and end of the isentropic expansion, and may be 
read directly from the Q-curves on the T0-chart (Plate I, Appen- 
dix) or from abscissas on the Mollier chart (Plate II, Appendix). 
The efficiency is 

Ef. = ^£— . . . (192) 

(q + xr + CpD)c - q% 
or / 

-/• = ^^ <-) 

This last form is the most convenient when the charts are used 
for obtaining A(2i and AQ%. These heat quantities are of course 
measured above 32° F. 

95. The Rankine Cycle, (a) This cycle is very similar to 
that last described, being obtained from it by a simple modifica- 
tion, the reason for which will be considered in a later chapter. 
The Rankine cycle, shown in Figs. 59 and 60 for dry steam at the 
beginning of expansion and superposed on the Clausius cycle for 
the same conditions, is seen to differ from the latter only in having 
the adiabatic expansion cut short by a constant-volume line de. 

Since the adiabatic line is not continued to the lowest tempera- 

* In solving for Dd it is necessary to assume a trial value of Cp and use the 
"cut and try method." 



74 



HEAT-POWER ENGINEERING 



ture in the cycle, the expansion is said to be incomplete. As the 
figures show, the area of this cycle is less than that of the one 



6 c 












1 












\ 




Rankine 










\ 












\ 










f 








d 












7-=.^^ 


la 








e 


' 




(XU)^ 


"^ 



Volumes 
Fig. 59. — PV-Diagram for Rankine Cycle with Dry Saturated Water Vapor at c. 









ib 




Ti 




lC 




















/ 










\ 








/ 




Rar 


kine 




\ 






c 


// 




Td 






icl\ 
\ 




2 
1 


7 




T2 


















'' 

































Entropies 
Fig. 6o. — T<^-Diagram for Rankine Cycle with Dry Saturated Water Vapor at c. 

having complete expansion, while the heat added along ab and be 
is the same in both. It therefore follows that the Rankine cycle 
must be still less efficient than the Clausius. Despite this fact, 



VAPOR CYCLES 175 

it is one of the most commonly used vapor cycles, being that 
approximated by most reciprocating steam engines. 

(b) During the constant-volume pressure drop, de, heat is 
given up irreversibly by the working material because the cold 
body receiving that heat must have a temperature at least as low 
as Te. Strictly interpreted, the line de on the T^-diagram repre- 
sents an equivalent reversible process. 

It is evident that all the heat given to the cold body is not 
rejected when the working substance has the same temperature 
as that body, and hence this cycle should have a lower efficiency 
than a similar Clausius cycle. This has just been shown to be 
the case. 

Work per Pound of Dry Saturated Steam Used in Rankine Cycle. 

(c) With vapor dry and saturated at the beginning of adia- 
batic expansion, the work per pound is 

AE=AQi-AQ2 (194) 

AE= \(q,-qa)]+r,] 

— I (Xdpd + qd) — {XePe + qe) + XeT^] B.t.U. . . (195) 

In this expression the difference {xdPd + qd) — (xePe + qe) is the 
difference of intrinsic energy possessed by the vapor at the points 
d and e. It is obvious that, to decrease the pressure at constant 
volume, heat must be abstracted, and since no external work, 
positive or negative, is done, all heat removed must come from 
the stock of intrinsic heat energy possessed by the material at d. 
To use Eq. (195), however, the two qualities Xg and Xd must be 
determined first. 

(d) A more useful expression may be developed as follows: 
Reference to Fig. 60 shows that the work of the cycle is repre- 
sented by the sum of areas fbcd and afde. The former area is 
the same as that of a Clausius cycle with temperature limits Ti 
and Td, and its heat value can be computed from Eq. (177). 
The area afde corresponds to the similarly lettered area in the 
PV-diagram, Fig. 59, and hence represents A {Pd — Pe) • (xu)d 
B.t.U. of work. Hence the work of the Rankine cycle for steam 
initially dry and saturated is 

AE = 1X1 -qf- ixr)d} + A(Pd - Pe) • ixu)d, . (196) 
and all quantities in this expression are either known at the 
outset or are obtainable directly from the Steam Table, with the 
exception of Xd, which can be obtained from Eq. (188) or (189). 



176 



HEAT-POWER ENGINEERING 



Efficiency of Rankine Cycle Using Dry Saturated Steam. 

(e) The heat received in this cycle is the same as that in the 
Clausius cycle, that is, 

AQi = Xi - 22- 
Hence the efficiency is 

^^_ _ AQi - AQ2 _ AE from Eg. (196) ^ ^^^^^ 

AQi Xi — 22 

96. The Rankine Cycle in General, (a) Starting with steam 
initially wet, the work done is 

AE = I (xifi + 2i - 2/) - Xdra] + A(Pci - P2) xaUa, . (198) 



bcic 



^^>.^d 



h 


Ci c 


/. 


chjk 


a ei e 



((X) steam Wet at C i and 

^ ' Dry at C 



l> 


(i Ci 






% 


-r^ 


a 


e 


ei 



ffA Steam Superheated Thiough- 
out Expansion from C i to cl 1 



h 


-•^...ci 




1 




^di 


a 


e 


ei 



/7,'\ Superheated Steam at Cl 
Expanded to Wetness at d 1 



he 



C^) Ether Taper Dry at C Becomes 

Superheated During Expansion C cL 



Fig. 6i. — Rankine Cycles — Various Cases. 



in which all quantities are known or are obtainable from the 
Steam Tables except Xd, which must be computed by using Eq. 
(i88) or (189). 

(b) In the most general case, having first determined from 



VAPOR CYCLES 



177 



the equation last mentioned the quaHty Xd (or superheat Dd) at 
the end of the adiabatic expansion, the work done is 

AE = {(q+xri- C^D), - g_f - i^r + C^Z)),| 

-hA(Pd-P2)Vd, (199) 

where Vd = (xV — 0.017)^ if the steam is wet at d, or Vd = 
(Vs — o.oi7)d if superheated. Vs can be found from Eq. (134). 



Ef. 



(200) 



{q+xr + CpD)o - ^2 

(c) As in the other vapor cycles, there are a number of different 
possibilities as regards the working substance, but every case can 
be worked out more or less simply by means of the expressions 
already developed. Various cases of the Rankine cycle are 
shown in Fig. 61. 

97. Cycle with Rectangular PV-Diagram. (a) This cycle is 
the least efficient of all the vapor cycles in practical use. It is 



6 c 
































\ 


















\ 
















\ 












«^-^ 






'"". 










, 








' 


■■----_ 






h 


d 












'1 



Volumes 
Fig. 62. — Cycle with Rectangular PV-Diagram. 

composed of two constant-pressure lines joined by two lines of 
constant volume, as shown in the PV-diagram, Fig. 62, and in 
the T(/)-diagram, Fig. 63. 

The diagrams show this cycle superimposed upon a Clausius 
cycle so chosen that the same weight of working substance is 
used in each. It is evident that the Clausius cycle will require 



178 



HEAT-POWER ENGINEERING 



a much larger cylinder than the cycle under consideration, but 

the work per cycle will also be much greater per pound of vapor. 

The T0-diagram shows that the heat absorbed is the same with 

both cycles, namely, the area beneath the line abc. The work 







b 


/ 








Xc 








/ 






/ 


^ 










/ 






" 




i \ 

1 \ 
1 \ 




g 






y" 








1 \ 






t 


^ 
























\ 





















Entropies 
Fig. 63. — T<^-Diagram for Rectangular PV Cycle. 

done is, however, greater with the Clausius cycle than with the 
rectangular PV cycle, as is shown by the inclosed areas of the 
diagrams. It follows that the efficiency of the cycle with rec- 
tangular PV-diagram must be less than that of the Clausius 
cycle. The Rankine cycle for the same heat input evidently 
gives an amount of external work intermediate between that 
obtained with the Clausius cycle and that obtained with the 
cycle under consideration, and must therefore have an inter- 
mediate efficiency. The rectangular PV-diagram may be looked 
upon as a limiting case of the Rankine cycle, the Clausius cycle 
being the other limit. 

Work per Pound of Dry Saturated Steam Used. 

(b) From Fig. 62 it is apparent that 

A£ - A{Pi - P2)u (201) 

Efficiency of the Cycle Using Dry Saturated Steam. 

(c) The heat received is the same as that in the Clausius cycle. 
Hence 

AE_AiP.-P.)u ^^^^^ 



Ef.= 



AQi 



(^1- 22) 



VAPOR CYCLES. 179 

98. The Rectangular PV Cycle in General. In any case 

AE = A(Pi - P2) XoU, (203) 

where XcM = {xV — 0.017)0 if the steam is wet, or = (Vs — o.oi7)<; 
if superheated. Vs can be found from Eq. (134). The general 
expression for the efl&ciency is 

Ef. = ~ — . . . . (204) 

(2 .+ xr + CpD)o - 22 



CHAPTER XIII. 

POWER, EFFICIENCY, AND PERFORMANCE. 

Certain general definitions which are necessary in the con- 
sideration of real engines are collected in this chapter. They 
will be discussed here very briefly; most of them will be con- 
sidered more fully in later chapters and some belong more prop- 
erly to the province of Experimental Engineering. 

99. Power, (a) In English-speaking countries, the foot- 
pound (ft. -lb.) is the unit of work generally used by engineers. 
The unit of power, or unit of the " rate " of doing work, is the 
horse power (h.p.) ; it equals the power equivalent to the doing 
of 33,000 foot-pounds of work per minute. 

Then the horse power developed by any apparatus is 

, _ Total ft. -lbs. of work developed permin. , . 

•P' ~ 33,000 ' ^^^^' 

The heat equivalent of one horse power is 

^"X 000 
One h.p. = ^^' = 42.42 B.t.u. per min. . . (206) 

778 

(b) If work is done for one hour at the rate of one horse power, 
the total work done is called one horse-power hour (h.p. -hr.). 

Then, oneh.p.-hr. = 33,000 X 60 = 1,980,000 ft.-lbs. . (207) 

1,980,000 



778 



= 2545 B.t.u (208) 



100. Distinction between Real and Ideal Engines. In con- 
sidering the ideal or thermodynamic engine in preceding chap- 
ters, a working substance was assumed to pass through cycles 
within a closed cylinder, and it was found that a certain amount 
of work, A£, would be delivered to the piston during each cycle. 
The material of the cylinder and piston was assumed to have 
certain properties which no available material really has. The 
cylinder and piston were assumed to neither absorb nor conduct 

180 



POWER, EFFICIENCY, AND PERFORMANCE 



l8l 



heat. The piston was supposed to be without leakage and 
friction; and any other necessary mechanism of the engine was 
assumed frictionless. These conditions cannot be reahzed in 
practice. Therefore, the action of a real engine must differ con- 
siderably from the conceived action of an ideal engine. 
Losses in real heat engines may be classified as follows: 
(i) Cycle loss, — for even with the ideal cycle only part of the 
heat supplied can be converted into work. 

(2) Cylinder losses, or those which occur within the real 
cylinder because the ideal cycle is not perfectly produced. These 
losses reduce the work actually delivered to the piston by the 
working substance. 

(3) Friction losses, occurring in the mechanism used in the 
transmission of work between the piston face and the place of 
utilization. 



loi. The Indicator. The work actually performed on the 
piston by the working substance in the cylinder of the real 
engine and the pressure-volume changes that actually occur 
within the cylinder can be 
determined by using the in- 
strument called the " Indica- 
tor," which can be made to 
draw the PV-diagram for the 
changes actually occurring. 
The comparison of such a dia- 
gram with the ideal one aids 
in determining the cylinder 
losses. 

This instrument is shown 
in Fig. 64. A card is mounted 
on the outside of a metallic 
cylinder which is caused to 
oscillate in unison with the 
motion of the engine piston. 
A pencil, which may be 
pressed against this card, is actuated by a small, spring-balanced 
piston subjected to the same pressure as the engine piston. 
Thus the card movement is proportional to the volume dis- 
placed by the engine piston, while the pencil movement is pro- 



i 


) 




ll 






JI3 


4-4 


im 




i|ilL 


'1 1 'lllll 


^^|I['M 


T 


1 


—Piston 

3 




i 


-^MLM 



Fig. 64. 



l82 HEAT-POWER ENGINEERING 

portional to the pressure which actuates the piston. The pencil 
movement is at right angles to the card movement, and hence 
a pressure- volume diagram with rectangular coordinates, such 
as abcde in Fig. 65, is drawn. If the card cylinder oscillates 
under the pencil while the indicator piston is disconnected from 
the engine cylinder and subjected to atmospheric pressure, a 
horizontal line, called the atmospheric line, will be drawn. 

102. The Indicator Diagram, (a.) In the pressure-volume 
diagram drawn by the indicator, as in the PV-diagrams pre- 
viously considered, the inclosed area represents the work done 
upon the engine piston by the working substance during the 
cycle. 

(b) The Pressure Scale, Sp, or pressure per inch of ordinate, 
equals the pressure in pounds per square inch of piston area 

corresponding to one inch 
3 movement of the pencil paral- 
^ lei to the pressure axis. This 
\ is also called the " Spring 
H Scale." 

I The datum of absolute pres- 

sures is a horizontal line, 00 
,7v^ ^piston-DiBpiacement ^ in Fig. 65, drawu at a distance 

Y ^Clearance , , , , . ,. 

below the atmospheric Ime, 
Fig 65 

A A , equal to the atmospheric 

pressure as measured on the pressure scale. Thus for any point, 

the absolute intensity of pressure per square inch of piston 

area = (ordinate above 00) X Sp] similarly, the pressure above 

atmospheric = (ordinate above A A) X Sp. The latter pressure 

is usually called the " gauge pressure." 

(c) The Volume Scale, Sv, equals the displacement of the 
piston in cubic feet per inch of abscissa. 

The datum of total volumes is a vertical line, YY in Fig. 65, 
located to the left of A a at a. distance representing, to scale, the 
" clearance volume " or space in the cylinder occupied by the 
working substance when the piston is at the beginning of its 
stroke. Thus for any point on the diagram, the total volume 
of working substance in the cylinder equals Sv X (abscissa 
from YY) , and the volume displaced by the piston is Sv X (ab- 
scissa from Aa). 



POWER, EFFICIENCY, AND PERFORMANCE 183 

(d) The Scale of Work, Sw, corresponding to one square 
inch of area of the diagram = S^ = Sp X Sv foot-pounds per 
square inch of piston area. 

The work done by the working substance upon the total 
piston area, as represented by the area of the diagram, is called 
the Indicated Work. Thus the i.w. = (area of diagram) X (area 
of piston) X Sn>. 

The corresponding rate of doing indicated work is expressed 
in terms of horse power; it is called the Indicated Horse Power 
(i.h.p.) and is comxputed by using Eq. (205). 

(e) Consider Fig. 65 as an actual diagram taken from an engine. 
From the point a the engine piston moved out until the point 
c was reached. By virtue of the property of the PV-diagram, 
the area between the lines abc and 00 represents the work done 
upon the piston by the expanding working substance. This 
work may be computed by multiplying the average pressure 
on the face of the piston of the engine by the piston's move- 
ment. To find the average pressure per square inch of piston, 
divide the square inches of area between abc and the pressure 
datum 00 by the length A A in inches and multiply this average 
height by Sp. Multiplying this mean intensity of pressure by 
the area of the piston in square inches and by the length of 
stroke of the piston in feet gives the work done during the out 
stroke of the piston. 

(f) Similarly, the area under the line cde represents the work 
done by the piston upon the working substance during the 
return stroke, and the mean ordinate of this area multiplied 
by Sp gives the average intensity of pressure against which the 
engine piston moved during this stroke. This, multiplied by 
the area of the piston in square inches and by the stroke of the 
piston in feet, gives the work in foot-pounds done by the piston 
ow the working substance during the return stroke. ^ 

(g) The useful work delivered to the piston during one cycle 
equals the difference between the work done upon it on the out 
stroke and that done by it on the working substance during the 
return stroke. 

The amount of work actually accomplished would have been 
the same if the difference between these two average pressures 
had acted upon the piston during one stroke only. The value 
of this difference is, however, given by dividing the area abcde by 



1 84 HEAT-POWER ENGINEERING 

the length of the diagram and multiplying by Sp. This is 
known as the mean effective pressure (m.e.p.), and is defined 
as the pressure which, operating on the face of the piston during 
one stroke, would do the same amount of work as is actually 
done per cycle by the variable pressure really acting. 

(h) In terms of the mean effective pressure, which will here- 
after be designated by pm, the work done upon the piston by 
the working substance, per cycle, is 

Work = ^^-o-L ft. -lbs., .... (209) 

in which a represents the area of the engine piston in square 
inches and L is the stroke in feet. 

If there are n cycles per minute, the work per minute will be 
n times the work per cycle, and the indicated horse power of 
the engine will be 

i.h.p. = ^^^ (210) 

33,000 

(i) Eq. (210) can be used to determine the diameter of cylinder 
needed to develop any i.h.p., provided the m.e.p., the length of 
stroke, and the number of cycles per minute are known. Thus 
the effective area of the piston must be 

a = 33,000 i.h.p. 

pmLn ^ ' 

from which the piston diameter follows. 

103. Methods of Determining the Area of an Indicator 
Diagram, (a) The area of an indicator diagram can be deter- 
mined (i) by placing transparent " cross-section paper " over 
the diagram and counting the squares surrounded; (2) by using 
some such form of mechanical integrating instrument as the 
" planimeter;" (3) by applying the " method of ordinates;" 
or (4) by using some integration rule such as the " Trapezoidal 
Rule " * and " Simpson's One- third Rule." f 

(b) One form of planimeter is shown in Fig. 66. It consists 
of two arms jointed together, one terminating in a " fixed point " 
which is a stationary pivot, while the other carries a '-' tracing 
point." The third support for the instrument is a point of the 

* For this rule see Kent's " Pocket Book." 

t See Church's " Notes on Mechanics " or Kent's " Pocket Book," pubhshed 
by John Wiley & Sons. 



POWER, EFFICIENCY, AND PERFORMANCE 



185 



rim of a graduated wheel or " record roller." If the record 
wheel is set at zero and the tracing point is moved clockwise 
around the outline of the diagram and is re- 
turned to its original position, the area of the 
figure is given by the reading of the record 
wheel. The theory and use of planimeters 
is treated in books on Experimental Engi- 
neering.* The mean ordinate is found by 
dividing the area by the length of dia- 
gram, and the m.e.p. is the product of the 
mean ordinate and the pressure scale. 

(c) In the method of ordinates, the length 
of the diagram is divided into a number of 
equal parts, with interval Ax as in Fig. 67, 
and ordinates are drawn, as 1,2, 3, etc., in 
the figure. Central intermediate ordinates are then drawn and the 
intercepts yi, yi, 3/3, etc., are scaled and used 
as the mean heights of the elementary areas 
-between ordinates. The area of the dia- 
gram is approximately A = l^y Y. Ax, and 





the mean ordinate is ym = 



^y 



Fig. 67. 



(no. of ordinates) 
This method is not strictly correct, for 
the middle intercepts are not necessarily the mean heights of the 
elementary areas. These mean heights can be found quite accu- 
rately by the method shown in Fig. 68. Here lines 
AB and CD (not necessarily horizontal) are so 
drawn that areas ai and 02 are equal and that hi =1)2. 
Then the distance y between the centers of these 
lines is the true mean height. The equality be- 
tween areas ai and 02 and between hi and hi can 
be estimated very accurately by eye. 

104. Delivered Power, (a) In Section 100 it 
was stated that only a part of the net work done 
on the piston by the working substance is delivered by the engine, 
as there is a friction loss in the moving parts. The power which 
actually is made available by the engine is variously called the 




* See Carpenter and Diederich's 
John Wiley & Sons. 



Experimental Engineering," published by 



1 86 HEAT-POWER ENGINEERING 

delivered horse power (d.h.p.). the brake horse power (b.h.p.), 
and the effective horse power (e.h.p.). 

The difference between the indicated horse power and the 
delivered horse power is a measure of the power lost in friction, 
and is called the friction horse power (f.h.p.). Then 

f.h.p. = i.h.p. — d.h.p (212) 

The indicated horse power can be determined by means of the 
indicator, and hence, if either the friction horse power or the 
delivered horse power can be measured, all three of the quanti- 
ties of Eq. (212) become known. 

(b) The direct measurement of the friction horse power is 
usually impossible, but several approximate methods are used. 
One scheme depends upon the assumption that the power con- 
sumed in engine friction is constant for all values of delivered 
power. This assumption is not accurate, but may be used for 
approximation. Assuming it true, the indicated horse power 
obtained when the 'engine is running at speed with no external 
load, that is, when all the indicated power is applied to overcome 
friction, may be taken as a measure of the friction horse power. 

Sometimes it is possible to drive an engine at its normal speed, 
from some external source of power, such as an electric motor or 
a shaft. When this can be done, and when the power thus con- 
sumed can be measured, it furnishes an approximate determina- 
tion of the friction horse power. However, it is necessary to 
make the same assumption as in the previous case. 

The usual method is to determine the delivered horse power 
experimentally and to calculate the friction horse power by 
Eq. (212). 

The delivered horse power may be measured by the use of a 
prony brake or similar absorption or transmission dynamometer; 
hence the term " brake horse power." For large engines ab- 
sorption dynamometers become elaborate and expensive and are 
seldom used except in special cases. 

105. Efficiencies, (a) Efificiency is the ratio of result to 
effort. For the heat engine there are several such ratios, which 
depend upon the meanings given to the terms " result " and 
" effort." They are useful in comparing performances of dif- 
ferent engines, in locating losses, and in showing opportunities for 
improvement. Unfortunately, there is lack of uniformity in the 



POWER, EFFICIENCY, AND PERFORMANCE 



187 



names applied to the various efficiencies, and in some cases the 
same term has been used for entirely different ratios. In the fol- 
lowing discussion the names which are apparently the most suit- 
able have been adopted. 

Fig. 69 is a diagram showing the energy stream. Here, as in 
Fig. 3, the width of stream shows the amount of energy still 
available for doing external work. As the stream progresses 
losses occur, as shown by the offshoots, and less energy remains 



e^ 


^^ 


23^ 






c?o 




III 



r3 W°- 




Fig. 69. 



available for doing external work. The several efficiencies, 
which will now be considered, may be studied in connection with 
this figure, and the relation between the various ones will be 
made clearer by referring to the figure as the discussion pro- 
gresses. 

(b) Carnot Efficiency. It has been shown that the efficiency 
of the Carnot cycle, and of all other reversible cycles, is the 
theoretical maximum with any given temperature limits. It is 
an ideal efficiency, but is impossible of attainment in any real 
case. Its value regardless of the kind of working substance is 



Efc- 



Ti 



(213) 



In Fig. 69, XZ represents the heat supplied and XY that 

which would be delivered as external work if the Carnot cycle 

XY 
were followed ; hence the Carnot Efficiency is Efc = -y^ • 



1 88 HEAT-POWER ENGINEERING 

(c) Cycle Efficiency. In all real engines the working sub- 
stance in its action approximates one of the theoretical cycles 
already developed. Each of these cycles was shown to have in- 
herent thermodynamic loss and a theoretical efficiency less than 
unity. This efficiency will hereafter be called the Cycle Effi- 

AB * 
ciency, CEf. It is shown in Fig. 69 by the ratio -^-p- 

For example, if a steam engine is assumed to follow the ideal 
Clausius cycle, the Cycle Efficiency is given by Eq. (192), and 
the work, A£i, per pound of material by Eqs. (188) to (191). 
In Fig. 69, ^5 represents AEi. 

No real engine actually attains the efficiency of its theoretical 
cycle because of unpreventable losses, but the Cycle Efficiency 
represents the best result attainable with the cycle in an engine 
having no extra-thermodynamic losses. 

(d) Relative Efficiency. It would seem that the engineer 
should be able to design and construct engines to operate with 
the Carnot and other reversible cycles, and thus approximate the 
ideal efficiency. However, practical reasons generally compel 
the use of engines approximating theoretical cycles that are 
thermodynamically less efficient. This reduces the possible 
efficiency even before the practical losses are considered. 

A measure of this reduction is obtained by dividing the Cycle 
Efficiency of the engine considered by the Carnot Efficiency. 
The quotient will be called the Relative Efficiency, REf, and is 

REf = ^. (214) 

Referring to Fig. 69, it is evident that 

^^-^ = [ac) -^{xzJ^Yy 

_ Work done by cycle under consideration 
Work done by Carnot cycle 

(e) Indicated or Cylinder Efficiency. In actual engines, as 
stated, the work done upon the piston by the working substance 
is of course always less than the theoretical quantity; that is, 

* Note that any engine operating on a cycle which is theoretically reversible will 
have a Cycle Efficiency equal to the Carnot Efficiency (as in (b)). In other cases 
the amount by which the CEf falls short of Efc indicates the theoretical disadvan- 
tage of the irreversible cycle. 



POWER, EFFICIENCY, AND PERFORMANCE 189 

it is less than the product of the Cycle Efficiency by the heat 
supplied. 

The ratio of work actually done to work theoretically possible 
measures the perfection of design, construction, and operation of 
the cylinder, piston, and valves. 

This ratio, which will be called either the Indicated or the 
Cylinder Efficiency,* lEf, can be expressed in several ways as 
follows : 

TTTf — ^^^^ *^f actual indicator diagram , , 

•' ~ Area of theoretical PV-diagram ••••'. 5 ; 



Indicated work per pound of working substance 
778 A£ (for corresponding theoretical cycle) 

Heat utilized per pound of working substance 
A£ (for corresponding theoretical cycle) 
I.h.p. 



Theoretical horse power' 



(215b) 
(215c) 
(2i5d) 



In the energy stream shown in Fig. 69, DE represents the indi- 
cated work and AB the theoretical work. Evidently the Cylin- 
der Efficiency is 

^^^ AB DF 

For example, if, in the case of the steam engine previously 

cited, the work per pound of steam shown by the actual indicator 

diagram is AE' , and if A£i is the work with the Clausius cycle, 

AE' 
then the lEf = — ^=r , and DE in Fig. 69 represents A£'. 

Aiti 

(f) Mechanical Efficiency. The ratio of work delivered by 
the engine to work received by the piston (equal to the ratio of 
delivered power to indicated power) is called the Mechanical 
Efficiency, MEf. Thus 

^^/-t^- (-'^) 

This fraction gives the proportion of the power received by the 
piston which actually becomes available as mechanical power for 
the consumer. The loss is a mechanical one due to friction of the 
mechanism. 

* This is also often called the " Potential Efficiency on the i.h.p.", and the " ther- 
mal efficiency ratio." 



190 HEAT-POWER ENGINEERING 

In Fig. 69, JK represents the energy delivered by the engine, 
and DE, or JL, shows the indicated work done on the piston; 

hence the mechanical efficiency is -jj ' 

J l-j 

(g) Thermal Efficiency on the I.h.p. The ratio of indicated 
work done (GH in Fig. 69) to heat supplied in the working sub- 
stance (XZ or GI) is useful in showing the combined efficiency 
of the cycle and the cylinder with appurtenances. It will be 
called the Thermal Efficiency on the i.h.p., abbreviated TIEf, 
and is 

^ Indicated work in B.t.u. , ^ 

Heat supplied to cylinder ' 

Obviously, this efficiency equals the product of the Cycle Effi- 
ciency by the Indicated Efficiency, that is, 

TIEf = CEf XlEf (218) 

fTJ 

The TIEf is shown in Fig. 69 by the ratio y^Y ' 

(h) Thermal Efficiency on the Brake or Delivered Power. 

The ratio of delivered work {PQ in Fig. 69) to the heat supplied 

the engine will be called the Thermal Efficiency on the Brake or 

Delivered Power, TDEf. Thus 

_^_ . Work delivered in B.t.u. , . 

TDEf = -^5 — 7 r^-3 TT— ] — • . . (219) 

Heat supplied cylmder 

Also, it is evident that 

TDEf = TIEf X MEf (220)^ 

PQ 
The TDEf is shown in Fig. 69 by the ratio -7^- 

PK 

(i) The Overall Efficiency of the Engine. The true efficiency 
of the engine as a whole, compared with the ideal or thermody- 
namic engine with the same cycle, will be called the Overall 
Efficiency, OEf. This takes account of both the cylinder and the 
mechanical losses.* Hence 

OEf = IEfxMEf (221) 

The OEf IS shown m Fig. 69 by the ratio -7-^ , or -^-r- • 

A3 MU 

A study of Fig. 69 shows that all of these efficiencies follow 
one another in logical order, and that each has a definite bearing 
upon the analysis of the performance of real engines. 

* This is also called the " Potential Efficiency on the d.h.p." 



POWER, EFFICIENCY, AND PERFORMANCE IQI 

io6. Engine Performance, (a) The relative performance of 
two heat engines can be determined by comparison of the amounts 
of heat used to produce a given amount of work. The unit of 
work usually adopted for comparison is either the indicated 
horse-power hour or the delivered horse-power hour. Thus the 
Rate of Heat Consumption may be defined as B.t.u. required per 

horse-power hour, that is, ; , . - or the , , ' ' ,' — , as the case 
i.h.p.-hr. d.h.p.-hr. 

may be. 

(b) If the amount of working substance used per hour is 
weighed and if the h.p. is determined, then the weight of mate- 
rial per h.p.-hr. can be computed. Evidently, if Wi, or Wd, is 
the weight of working substance per h.p.-hr., and if AQ is the 
heat per pound of material, then 

ix^=«''x^e (-.) 

d^. = ^^^^e (-3) 

Since the equivalent of one h.p.-hr. is 2545 B.t.u., and since the 
Thermal Efficiency is the ratio of the work actually done to the 
heat supplied, it is evident that 

B.t.u. ^ 2545 _ 

h.p.-hr. TIEf, or TDEf, as the case may be • • v 4; 

If several engines use working substances of the same kind 
with the same heat content per pound, the relative performances 
can be found by comparing the Rates of Consumption of Work- 
ing Substance (i.e., pounds per i.h.p.-hr. or per d.h.p.-hr.). These 
values are known as Engine Economies. 

Further, if unit weights of these working substances receive 
their store of heat from equal weights of fuel, the Rates of Fuel 
Consumption (pounds per i.h.p.-hr. or d.h.p.-hr.) may be used for 
comparison. 

(c) Graphical representations of engine performances are often 
very useful. They may be based upon the scheme shown in 
Fig. 70, which applies to an impossible machine supposed to con- 
vert into mechanical energy all of the heat supplied it ; — thus 
it is the case with efficiency of 100 per cent. 

Since 2545 B.t.u. are equivalent to one h.p.-hr., and since in 
this case the efficiency is the same at all rates of power develop- 



192 



HEAT-POWER ENGINEERING 




ment, that is, at all " loads," the curve showing the Rate of Heat 
Consumption, or R-curve, is a horizontal line with ordinate 2545 

B.t.u., as shown in the figure. 
The scale for this line is at the 
right. 

The Total Heat Consumption 
per hour at any load is the pro- 
duct of the horse power and the 
corresponding rate. Thus the 
curve showing the Total Con- 
sumption, or the TC-curve, re- 
sults from plotting the products 
of corresponding abscissas and 
ordinates of the R-curve. Since 
the latter is a horizontal line in this case, the corresponding 
TC-curve must be a straight line passing through the origin and 
with slope corresponding to the rate. The scale for this curve is 
given at the left of the figure. 

(d) When the B.t.u. per pound of working substance remains 
constant, it is sometimes convenient to construct curves similar 
to those in Fig. 70 but for the consumption of the working sub- 
stance instead of B.t.u. Thus the R-curve would represent the 
Rate of Consumption of Working Substance (as pounds of steam 
per h.p.-hr., or cubic feet of gas per d.h.p.-hr., etc.), and the 
TC-curve would represent the total consumption of working sub- 
stance (as total weight of steam or cubic feet of gas per hour) . 

Sometimes similar curves are drawn to represent the rate and 
total consumption of fuel used (as pounds of coal per h.p.-hr., 
and total weight per hour) . 

(e) According to assumption the efficiency of this impossible 
device is constant, and if the efficiency line were drawn it would 
be horizontal at a height corresponding to lOO per cent. Even 
in the best theoretical cycles, that is, the Carnot, and the other 
reversible ones, the work performed is very much less than the 
mechanical equivalent of the heat supplied, and the efficiency is 
always much less than unity. 

(f) In the real engine the efficiency, and hence the rate, 
instead of being constant, varies characteristically with the load ; 
thus, instead of being straight, as in Fig. 70, the lines representing 
the efficiency and rate may be curved, as is shown for one real 



POWER, EFFICIENCY, AND PERFORMANCE 



^93 





E 


/ 


> 




-^ 


^ / 


1 

1 

1 





100 H 200 

Horse Power 



engine in Fig. 71. Further, the TC-curve will not pass through 
the origin of coordinates, but will have a positive intercept on 
the Y-axis, as shown in Fig. 71. This is because there is a heat 
loss when the external load equals 
zero; for, even when an engine is 
running without delivering power, 
there is heat lost in radiation and 
conduction and in overcoming fric- 
tion, and if the engine is motionless ^ 
at the operating temperature, there 
is still the loss due to radiation and 
conduction. 

(g) The ordinate scales in Fig. 
71, as in the case of Fig. 70, may 
be made to read, in thermal units, ^'S' ^^' 

pounds of working substance or pounds of fuel. 

The ratios of the number 2545 to the different ordinates of 
the heat-rate curve evidently give values of the Thermal Effi- 
ciencies at different loads, as shown by the curve Ef in Fig. 71. 
This curve will give either the TIEf or the TDEf, according to 
the basis used in determining the R-curve. Also, the Thermal 
Efficiencies are given by the ratios of ordinates in Fig. 71 to 
the corresponding ones in Fig. 70. 

Similar comparisons between the curves for any theoretical 
cycle with those for the Carnot cycle will give the Relative 
Efficiencies for the former. 

(h) In Fig. 71 a dotted line is drawn from the origin tangent 
to the TC-curve. The point of tangency, Z, determines the 
abscissa, or horse-power output, at which the efficiency is maxi- 
mum and the rate minimum. Evidently, the best economy is 
obtained when the engine develops this power, and, other things 
being equal, an engine should be of such size as to operate most 
of the time at or near this load. If the engine normally fur- 
nishes more or less than this power, it is either too large or too 
small from the standpoint of economy only. It will appear later, 
however, that many other considerations enter into the choice 
of size of engine best suited for a given set of conditions. 



CHAPTER XIV. 

THE THEORETICAL STEAM ENGINE. 

107. General, (a) In the actual steam engine only a por- 
tion of the heat supplied in generating the steam is converted 
into useful work. This portion at maximum is only about 25 
per cent and ordinarily is from 5 to 12 per cent. All the rest 
of the heat, from 75 to 95 per cent, is lost, and represents a pro- 
portionate waste of fuel and of money spent for it. It is very 
important for one who is to be connected with steam engineering 
to understand why this great loss occurs and how it can be 
minimized. 

(b) The greater part of the heat loss would occur even in 
the theoretically perfect engine, — because of imperfections 
inherent in the ideal cycle; and the exact extent of the loss in 
this case can be readily computed. The further losses that 
occur in the actual engine are due to physical imperfections; 
and their amounts can be determined experimentally, while 
their causes and proportionate distribution can be studied by 
comparing the actual cycle with the ideal. Many of the losses 
can be determined by comparing the actual cycle with the ideal 
ones, — the Carnot, Clausius, and Rankine. 

108. The Carnot Cycle and the Steam Engine, (a) As the 
Carnot cycle (Section 91) gives the greatest possible efficiency, 
it would seem to be the most desirable cycle to use in any type 
of engine. 

Heretofore, in discussing this cycle, it was assumed that all 
operations were performed within a single nonconducting cyl- 
inder, to the end of which could be attached the hot body, or 
the cold body, or the nonconducting head, as required during 
the cycle. While such an arrangement is conceivable, it cannot 
be realized materially, and to obtain an apparatus of practical 
value it is necessary that some parts of the cycle shall be per- 

•194 



THE THEORETICAL STEAM ENGINE 195 

formed outside of the cylinder. In this latter case, however, 
the result will be the same, provided the cycle is carried through 
in the same manner as before. Thus the cycle may be per- 
formed in the following apparatus: 

(b) Let the cylinder, the cylinder end, and the piston be per- 
fectly nonconducting, and let the cylinder end be permanently 
attached. Then, instead of a hot body, let there be a pipe with 
a valve (" Steam Valve ") connecting the cylinder to a boiler 
which will supply steam (heat) at the constant temperature Ti^ 
corresponding to pressure pi; and in place of the cold body let 
there be another pipe with a valve (" Exhaust Valve ") con-^ 
necting the cylinder to the condenser, in which the temperature 
is maintained constantly at Ti, corresponding to the exhaust 
pressure p2. Such an arrangement, with the addition of a feed 
pump to return the condensate from the condenser to the boiler, 
completes the apparatus, which contains the simple elements of 
a steam power plant. 

(c) In performing the Carnot cycle, note that (see Section 53) : 
(i) All heat from the external source must be received at the 

constant temperature Ti of the source. 

(2) All heat discharged to the cold body must be rejected at 
the constant temperature Z2 of the cold body. Hence: 

(3) Before heat is received at the upper temperature Ti, the 
working substance must be brought to that temperature with- 
out receiving heat energy from the outside ; so 
it must be done by adiabatic compression from 
T2 to Ti, and 

(4) Before heat is rejected, the temperature 
must be lowered from Ti to T^ without losing 
heat as such to the outside; so this must be 
accomplished by adiabatic expansion. 

Referring to Fig. y2 (a) for theTV-diagram 
and to Fig. 72 (b) for the T0-diagram (the 
two figures being lettered alike), the cycle 
would be performed in the following manner: ^ig- 72- " 

(d) Isothermal Expansion (line ab). Since in the Carnot 
cycle the working substance must receive all its heat from the 
outside source at the upper temperature Ti, the cycle must begin 
with water (say one pound) which has already been raised to 
this temperature. In the first operation, — starting with the 



a h 
\ T: V 

^t T2 \ 




d 


■^c 



a Ti 


6 


/ 


\ C6) 
\ 


/ d To 


\ 



196 HEAT-POWER ENGINEERING 

steam valve open, the exhaust valve closed, and piston against 
the cylinder head, — the boiler will supply the latent heat (at 
a constant temperature) to form the vapor, which will then 
occupy the volume Vb, the piston meanwhile moving out until 
it has swept through a volume equal to this. This first part of 
the cycle constitutes the period of admission. The steam valve 
is then closed, and the steam supply is " cut off " at point b. 

(e) Adiabatic Expansion {be in the figures). The steam is 
then allowed to expand adiabatically from b to c, within the 
cylinder, doing external work by moving the piston against a 
resistance until the temperature T^ of the condenser is reached. 
The pressure is then p2, the volume is Vc, and the piston is at 
the end of its stroke. This completes the second part of the 
cycle. The exhaust valve is then opened to " release " the 
steam from the cylinder, allowing it to flow to the condenser. 

(f) Isothermal Compression (cd). On the return stroke 
the piston drives the steam out of the cylinder into the con- 
denser, where, by the abstraction of heat, it is liquefied. During 
this operation the temperature remains constant at T^, so the 
heat is rejected to the cold body isothermally at the lowest 
temperature, as in the Carnot cycle. This completes the third 
part of the cycle and constitutes the period of " exhaust." 

So far the Carnot cycle has been followed without variation. 

(g) Adiabatic Compression (da). To complete the cycle, 
adiabatic compression should begin at the point d, so selected 
that when the piston reaches the end of the stroke, all of the work- 
ing substance will be returned to the initial condition. But since 
a part of the steam has been reduced to water in the condenser 
and is no longer in the cylinder, it appears that the cycle can- 
not be completed by any process entirely within the cylinder 
itself. 

It is possible, however, in theory at least, to complete the 
Carnot cycle by using a combined vapor-and-water pump, 
which, when the point d is reached, will receive all the water of 
condensation from the condenser and the vapor remaining in 
the cylinder at the point d, and by compression complete the 
condensation of the vapor, and bring the whole charge back 
to the initial condition by a process that is strictly adiabatic. 
But while this is conceivable it would be very difficult to carry 
out without introducing practical evils which would more than 



THE THEORETICAL STEAM ENGINE 197 

counterbalance the thermodynamic advantage. In practice 
this last operation would be omitted, and, instead, the steam 
would either be expelled from the cylinder and condensed in 
a " condenser " or else exhausted into the atmosphere. The 
water of condensation, or an equivalent amount of " make-up 
water," is then pumped to the boiler, where the heat is added 
to bring the temperature gradually back to the initial value, 
which is not in accordance with the requirements of the Carnot 
cycle. 

(h) It is true that in the actual steam engine compression 
is employed, but this must not be confused with the adiabatic 
compression of the Carnot cycle. But little of the steam is 
involved in this operation, and it is used principally for the 
purpose of " cushioning " the reciprocating parts in order to 
make the engine operate quietly. It has little effect on the 
thermodynamic operation of the engine. 

(i) Although the Carnot cycle is not ordinarily followed by 
the steam engine, it is often very useful to determine the efficiency 
and the work that would be done with this cycle, within the 
temperature range of the steam engine, in order to find the 
maximum output that could be theoretically attained by any 
engine, using any kind of working substance with the same 
temperature limits. 

Previous discussion of this cycle (Section 92) showed that for 
saturated steam the Carnot Cycle Efficiency, Efc, is given by 
Eq. (170), that the heat available, AQi, can be computed by 
Eqs. (172) to (174), and that the work done is A£ = ^Ql X Efc 
from Eq. (171). 

Since superheat is supplied in practice with gradually in- 
creasing temperature, the Carnot cycle is not a satisfactory 
standard for comparison for engines using superheated steam, 
and hence this case will not be considered. 

(j) As one h.p.-hr. is equivalent to the expenditure of 2545 
B.t.u., and as each pound of steam makes available A£ B.t.u. 
for doing external work, the Rate {W) of Steam Consumption 
per h.p.-hr., with the Carnot cycle, is evidently 

IF = ^ ...... . (225a) 

- '54^- . . . (225b) 



A(2i X Efo 



198 



HEAT-POWER ENGINEERING 



40 






t2 


=^o^ 


— 









4> 


C^ 


^t^ 


^ 






A 


r^." 




te 


53^- 





1 ^" 


// 




-ejeB^ 


■ — 






7 


v^ 










■^10 


A 




E 


Rcien 


cy 




/ 

Initif 


1 Pressu 


;e(AbsO 


Dry Sat 


rated S 


earn 


1( 


2 


30 3 


JO 4 


5 


)0 60 



(k) In practice some steam engines " exhaust " to the atmos- 
phere, with the temperature of heat rejection theoretically- 
equal to 212° F., corresponding to an absolute pressure of 14.7 
pounds per square inch; while other engines exhaust to a con- 
denser maintaining a vacuum of about 26" of mercury, the 

absolute pressure being a 
little less than 2 pounds per 
square inch and temperature 
about 125° F. The steam 
turbine, which is one form of 
steam engine, is often oper- 
ated with a vacuum of about 
28" of mercury or a little less 
than one pound " back pres- 
sure," the temperature being 
about 100° F. 

(1) Fig/ 73 shows curves 
of efhciency, B.t.u. of work 
per pound of steam, and 
water rate, for the ideal en- 
gine operating on the Carnot 
cycle with steam initially dry 
saturated and with the three 
exhaust pressures mentioned 
above. A scale for satu- 
ration temperatures corre- 
sponding to the different 
initial pressures is also 
given. 

(m) These curves show 
clearly that better results 
are obtained by increasing 
the initial temperature (or 
pressure) and by lowering 
the temperature (or pressure) 
of exhaust. A given temperature difference low on the tempera- 
ture scale gives better efficiency than the same temperature 
difference at a higher range, as the denominator Tx in Eq. (170) 
is lower. It is therefore theoretically advantageous to have Tt 
as low as possible in any case. 




Initial-Pressure (Abs.) Dry Saturated Steam 

Fig. 73- 



THE THEORETICAL STEAM ENGINE 



199 



109. The Regenerative Steam-Engine Cycle, (a) The T^- 
diagram, Fig. 74, shows that if hci is drawn parallel to the 
water line adi, the area abcidi will equal the area abed of the 
Carnot cycle. Thus, if 
steam is carried through 
the cycle abcidi, and if heat 
is received only along the 
line ab, as in the Carnot 
cycle, the two cycles must 
have equal efficiencies. 

(b) The cycle abcidi, 
called the Regenerative 
Cycle, can be obtained un- 
der ideal conditions in the 




Fig. 74- 



following manner : While the steam is expanding an infinitesimal 
amount from b, with drop in temperature from Ti to (Ti — AT), 
let a sufficient quantity of the steam, or heat from the steam, be 
abstracted from the cylinder to cause the expansion to be along 
bbi ; and let this heat be used to raise the feed water from ( Ti — A T) 
to Ti, changing the water from condition ai to a. The heat ab- 
stracted from the cylinder during this process is shown by the 
area below hb; and that given to the water, by the equal area 
below aia. Similarly, while stearn expands through another 
increment, &i to 62, let sufficient heat be abstracted from the 
cylinder to raise the water from condition 02 to ai. Continue 
this process for each increment of expansion until the final 
temperature T2 is reached. In this way the expansion bci is 
made parallel to adi. Obviously, in each instance when heat 
is supplied to or abstracted from the working substance, the 
transfer is at a constant temperature (considering the A 2" as 
insignificantly small). Thus the surrender of heat by the 
steam and the reception of heat by the water correspond to 
the regenerative action in the Joule and the Stirling gas cycles. 
After the water has thus been brought to condition a, the boiler 
can supply the latent heat for vaporization at the constant 
temperature Ti; and when expansion has reached the point Ci, 
the heat is rejected at constant temperature T2. 

(c) As the reception of heat from the hot body and rejection 
of heat to the cold body are thus all isothermal and reversible 
processes, and as the temperature changes are equivalent to 



200 HEAT-POWER ENGINEERING 

adiabatic ones, this cycle is the equivalent of the Carnot cycle, 
and the equations of Section 92 and curves given in Section 108 
for the latter can also be used for this Regenerative cycle. 

(d) This Regenerative cycle has been used but little in 
practice. It is approximated in some engines built by Nord- 
berg,* in which the steam is expanded in steps, by passing it 
successively through several cylinders. The theoretical expan- 
sion in the first cylinder corresponds to bb' in Fig. 74, but with 
a finite instead of an infinitesimal temperature drop; that in 
the second cylinder to bib"; and similarly for the expansions in 
each of the other cylinders. Heat represented by the area 
below bib' is abstracted from the steam from the first cylinder, 
(or from its steam jacket) and is used to raise the water from 
state a" to a'; heat corresponding to the area below 626", with- 
drawn from the second cylinder, raises the condition of the 
water from a'" to a"; and similarly from each of the other 
cylinders, heat is transferred to the water. Thus heat is ab- 
stracted by steps from the expanding steam and is used for 
progressively heating the feed water in small increments, each 
with but small rise in temperature. If these increments could 
be made infinitesimal, the heat additions would be isothermal 
and the Regenerative cycle would result. Nordberg used four 
steps only, but the remarkable results obtained with these 
engines when the heaters were in use, as compared with their 
performance without the heaters, seem to indicate that there 
may be considerable advantage to be gained by using the regen- 
erative principle even with but few steps. One Nordberg 
engirje attained 73.7 per cent of the efficiency of the Carnot 
cycle for the same temperature limits. 

no. The Clausius Cycle, (a) The theoretical cycle, approxi- 
mated by the ordinary steam engine, as was shown on pp. 195- 
197, is as follows: The working substance, starting as water at 
the boiling point, receives heat isothermally during the process 
of vaporization ; it then expands adiabatically from the higher to 
the lower temperature; it is next condensed isothermally; and 
finally, after being returned to the boiler, is brought back to 
the initial state, not by adiabatic compression, but by the ap- 
plication of heat. This cycle will be recognized as the Clausius 
cycle (Sections 93 and 94), and not only is it the theoretical 
* Transactions A. S. M. E., 1900, p. 181, and 1Q07, p. 705. 



THE THEORETICAL STEAM ENGINE 




50 100 150 200 2i 

Initial Pressure Lbs. Sq. In. ALs. 



cycle of the steam engine, but also that of the steam turbine, 
as will be seen later; it therefore is of value not only in com- 
paring the performances of steam engines with each other, but 
also in comparing engines with turbines. 

(b) The Clausius cycle, with the lower temperature taken as 
that of the exhaust steam, has been adopted by the British Institute 
of Civil Engineers* as the 
standard of comparison for 
steam engines and turbines, 
but is called by them the 
"Rankine cycle," t it having 
been published simultane- 
ously but independently by 
both Clausius and Rankine. 
The use of this temperature 
is also recommended by the 
American Society of Me- 
chanical Engineers in their 
" Rules for Conducting 
Steam- Engine 'Tests, "I as a 
standard when the engine by 
itself, and not the other ap- 
paratus of the power plant, 
is to be analyzed. 

(c) The work in B.t.u. per 
pound of steam (A£) can be 
computed for this cycle by 
using [Eqs. (i88) and (191), 
or it can be found directly 
and more conveniently from 
the Mollier chart, Plate II, 
in the Appendix. (For ac- 
curate results a larger chart 
should be used than is there 
given.) 

The efficiency of the Clau- 
sius cycle can be computed from Eq. (192) or (193). 

* Proceedings, 1898. 

t Note that the name " Rankine cycle " is used in this book to designate a 
different cycle, i.e., the Clausius with incomplete expansion. 

X Transactions, 1903, p. 716. 







.J^ 




^: 


/, 


^ 


-1;^ 


5^ 


Atmo^ 


Fres. 


/ 


^ 


J^ 


Wort 


Done 




/ 












5 


1 


1 


2 


2 


30 



Initial Pressure Lbs. Sq, In. Abs. 




Fig. 75-- 



Initial Pressure Lbs. Sq. In. Abs. 

Clausius Cycle. Dry Saturated 
Steam. 



202 HEAT-POWER ENGINEERING 

(d) Fig. 75 gives curves for the efficiencies, water rates, and 
work in B.t.u. for the three cases that were considered with the 
Carnot cycle, Section io8 (1), namely, with atmospheric exhaust 
pressures and with vacuums of 26" and 28" Hg, 

(e) A comparison of these curves with those for the Carnot 
cycle (Fig. 73) shows lower efficiency in this case, as would be 
expected. The work per pound of steam is larger, however, 
which at first seems wrong, but which is explained by the fact 
that the heat supplied per pound from the source is much larger 
in the Clausius cycle than in the Carnot, being (xr + q)i — g^ 
for the former as against xi^i for the latter, when dry saturated 
steam is used. Thus with the Clausius cycle less weight of 
steam is used per h.p.-hr., but each pound receives more heat and 
this is used less efficiently than with the Carnot cycle. 

(f) Comparing the Clausius cycle efficiencies when the steam 
is superheated with those when it is dry saturated (other condi- 
tions of operation remaining the same) shows that with superheat 
the efficiencies are so little higher that superheating would seem 
hardly worth while, when the additional expense of equipment 
and maintenance of superheating apparatus are considered. It 
will be seen later, however, that superheating may give beneficial 
results which are not in any way connected with the theoretical 
cycle, hence it is frequently used in steam-engine practice. 

III. The Rankine Cycle, (a) In the reciprocating steam 
engine, instead of expanding to the point 
\ di, Fig. 76, it is the general practice to dis- 

\ («) continue at some point d, and release the 

v. >wl u. steam at constant volume, along the line 

I "--^^ "i de, as is done in what has been previously 
e ^ called the Rankine cycle (Sections 95 and 

Ve Vdi 96). The " toe " of the diagram is thus 

b c cut off and the work represented by the 

r r?)') ^^^3^ ^^1^ is lost. The reason for sacrific- 

^ ^^f' ing this work is twofold: (i) By reduc- 

e ^ ing the maximum volume involved, that 

is, from Vdi to Vg, the size of the cylinder 

is proportionately decreased, and this re- 
sults in material reduction of the size 
and cost of the engine. (2) There is a loss in power and effi- 



THE THEORETICAL STEAM ENGINE 



203 



ciency if expansion is carried beyond the pressure that is just 
sufficient to overcome the frictional resistance of the engine; for 
in Fig. 76 (a), if expansion were completed, the additional work 
done by the steam is shown by the area eddi ; whereas, if de repre- 
sents a pressure equal to the mean frictional resistance of the 
engine, the additional work in friction, with the greater piston 
movement df, would be given by the area edifd, which is greater 
than the useful area eddi, by the area dfdi. The latter area 
represents the net loss accompanying an increase in expansion 
from d to di. 

(b) In the steam turbine, which has very little mechanical 
friction, the expansion is continued down to the exhaust pressure, 
as in the Clausius cycle. That the reciprocating steam engine 
does not do the same is a fault chargeable against it and one that 
cannot be entirely remedied. Hence, as a standard of compari- 
son for both the steam engine and the turbine, the Clausius 
cycle is preferable to the Rankine, and for that reason the latter 
cycle will not be further considered here. 

112. Clearance and Compression, (a) In the theoretical 
cycles previously discussed it was considered that no steam space 
existed between the cylinder head and the piston at the begin- 
ning of the stroke, and hence that the initial volume of steam in 
the cylinder was zero. In practice, however, 
the piston must not touch the cylinder head, 
and the shortest distance between them is 
called the " mechanical clearance,'' with values 
from \ inch to f inch or more. The cubical 
contents of this space, including the passages 
to the valves and all other spaces that must 
be filled with steam before the commencement 
of the stroke, is termed the " clearance vol- 
ume." It equals the initial volume on the 
PV-diagram, as shown by cl in Fig. 77. The 
percentage of " clearance volume " as com- 
pared with the piston displacement, or volume 
displaced by the piston per stroke, is from 2 
to 15 per cent in practice.* 

* The term " clearance "is used rather loosely as applying either to the linear 
or volumetric quantity, but the kind of clearance meant is usually apparent from 
the context. 



■eh 




(a) 








xk 


r\- 




'1 

xl> 


'\V"' 







Fig. 77- 



204 HEAT-POWER ENGINEERING 

(b) The clearance theoretically influences the amount of steam 
heat consumed per unit output of work. If the engine operates 
with a theoretical PV-diagram of rectangular form, Fig. 77 (a), 
the clearance space must be filled with steam each cycle, before 
the piston starts, and as this steam is exhausted with that which 
performs the work, it theoretically represents a direct waste, the 
percentage of waste being equal to the percentage of clearance 
volume. 

(c) If the cycle is that shown in Fig. 77 (b), a still greater pro- 
portion of the steam heat is wasted because of the clearance 
space; for in this case the clearance volume is greater in pro- 
portion to the total volume of steam admitted than in the pre- 
ceding instance. 

(d) If the cycle followed is that shown in Fig. yj (c), in which 
there is adiabatic compression along ab, there is theoretically no 
loss due to the clearance ; for at each stroke the weight of steam 
entrapped at a and compressed along ab can be considered, dur- 
ing expansion, as following back along ba, just as if this amount 
of steam were separated from the rest by a flexible diaphragm 
and were compressed and expanded adiabatically without being 
exhausted from the cylinder. 

(e) If the compression is not carried 

I V to the initial pressure, but is along some 

I \. line ka in Fig. 78, the case is intermediate 

V ^Vi between (c) and (d). If, in addition, the 

\ L_j--^(ii expansion is incomplete, terminating at 



Pj g some point d in Fig. 78, the clearance loss 

is theoretically a minimum when com- 
pression is carried to a point somewhat below b* 

(f) In the actual case there are certain influences to be dis- 
cussed later, which modify the theoretical effect of compression. 
Whether or not compression in the actual engine improves 
the steam consumption is still a matter of discussion. The 
influence is so small that the effect is difficult to determine 
experimentally. 

113. Cushion Steam and Cylinder Feed, (a) It is sometimes 
convenient to consider the weight of working substance present 
in an engine cylinder as composed of two parts, namely, that 

* See Heck's " Steam Engine," Vol. I, p. 97. 




THE THEORETICAL STEAM ENGINE 205 

entrapped during compression and that fed from the boiler during 
each cycle. 

(b) The steam entrapped during compression is called the 
" cushion steam." It is difficult to determine its quality through- 
out compression, but it is customary to assume it dry when com- 
pression begins. Since almost immediately after release the 
steam pressure drops to the back pressure, 
there is but little steam in the cylinder 
soon after the beginning of the back stroke. 
That part subsequently trapped in the 
clearance and compressed is subject to the 
higher temperature of the cylinder walls 
throughout nearly the whole of the return ^'§- 79- 
stroke, hence must be practically dry when compression begins. 

With this assumption, the weight of the cushion steam at k,. 
Fig. 79, can be computed from 

Wfc = Ffc -^ V;fc (226) 

in which Vk can be scaled from diagram and Yk is the specific 

volume, as given in the Steam Tables, for the pressure ^2 existing. 

If the same weight of steam is raised to the initial pressure pi_ 

and is maintained dry and saturated, it will occupy the volume 

Vb' =WkXVu (227) 

where Vi is the specific volume at the initial pressure pi. The 
volume Vb is shown by the abscissa at the point b' in Fig. 79, 
in which b'k is the saturation curve for a weight of steam equal 

to Wk. 

Evidently when the valve opens to admit steam to the cylinder 
this weight Wk is already present, and it occupies the volume Vb 
as soon as its pressure is raised to that of the entering steam. 

(c) The steam that is supplied to the cylinder from the boiler 
at every cycle is called the " cylinder feed" (w/). The cylinder 
feed may be determined by finding the weight of steam delivered 
to the engine in a given time and dividing this by the correspond- 
ing number of cycles. 

If the boiler, without loss, furnishes to the engine all the steam 
it generates, the weight of steam supplied is equal to the weight 
of water fed to the boiler in the given time. If a surface con- 
denser is used, w/ can be determined from the weight of the 



206 HEAT-POWER ENGINEERING 

steam condensed in the given time, provided there is no leakage 
in the condenser. 

In Fig. 79 the volume of the cylinder feed is shown by the 
distance b'c. It would be represented by be only in case the 
compression terminated at point b. 

(d) The total weight (w) of steam in the cylinder during 
expansion is evidently made up of the cylinder feed (w/) and the 
cushion steam (wk) ; thus w = Wf -{- Wk. Its theoretical volume 
at the time of cut-off, if it is dry and saturated, is Vc = w X Vc, 
where Vc is the specific volume of the steam at the cut-off pressure. 

114. Saturation and Quality Curves, (a) If the weight of 
steam (w) present in the cylinder is considered to be dry and 
saturated, it occupies at any time a volume F, = wY, where V 
is the specific volume for the pressure under consideration. By 
plotting on the PV-diagram the values of Fs for different pres- 
sures, a Saturation Curve is obtained. Such a curve is shown by 
€S in Fig. 80, and is of value in determining the quality of steam 
at different points during expansion (Section 70). For example, in 
Fig. 80, in which the expansion line cd is adiabatic, the quality 

AC 
of steam at any point C is x = -j-^, and the "wetness factor" is 

(b) If qualities are determined for several points along the 

expansion line and are plotted as ordinates on the corresponding 

volumes, as in the upper part of Fig. 80, 

' ^ a Curve of Qualities is obtained, which 

109 f' T'-<:^ltr shows how X varies during the expansion. 

■ j P° I V The quality curve in this case shows the 

I I I condensation that takes place in order to 

b c' c \ ] I make heat available for doing external 

\ V^i I work during the adiabatic expansion. In 

-L y--Si(^».|s the figure the steam is assumed to be dry 

\. \, rfj"~~-s and saturated at c, hence the saturation 

fc° I V curve must pass through that point, 

-^ Quality curves for any other kind of ex- 

^^' pansion line can be found in the same 

. AC . 
way; thus, if c'y is the line, the quality at C is-j-^, if the weight 

of material present is the same as before. 



THE THEORETICAL STEAM ENGINE. 



(c) Should the expansion hne cross the saturation curve, as 

in Fig. 8i, the quahty ratio would be greater than lOO per cent, 

which would indicate that the steam becomes superheated during 

expansion. If the weight {w) of steam is 

known, the specific volume of the super- 

V 
heated material follows from V = — , in 

w 

which V is the volume scaled on the dia- 
gram. Then the absolute temperature of 
the steam may be computed by solving 
Tumlirz's Eq. (134). Thus T = ^ (V + 0.256) 4- 0.5962, in which 
p is the absolute pressure in pounds per square inch. By sub- 
tracting from T the absolute temperature of saturation at the 
pressure p the degrees of superheat D can be found. 



c 



Fig. 



CHAPTER XV. 
ACTION OF STEAM IN REAL ENGINES. 

115. Cylinder and Thermal Efficiencies of the Steam Engine. 
(General.) (a) The actual behavior of the steam in a cyhnder is 
quite different from the theoretical, because of modifications of the 
ideal cycle, heat interchanges between the steam and the cylinder 
walls, and leakage of valves, piston, etc. The greater the per- 
fection attained in the design, construction, and operation of the 
engine, cylinder, piston, valves, etc., the closer will the actual 
behavior approach the ideal. The measure of this perfection is 
given by the indicated or cylinder efficiency (/£/), Section 105 (e), 
which can be computed by Eq. (215), or by the following: 

Actual B.t.ii. of indicated work per lb. of steam _ Hi , , 
Theoretical B.t.u of work with Clausius cycle AE 



(228b) 
(228c) 



_ B.t.u. equivalent of 1 i.h.p.-hr. _ 2545 

Heat available per i.h.p.-hr. Wi A£ 
_ Theoretical lbs, of steam per h.p.-hr. _ W 
Actual lbs. of steam per i.h.p.-hr. Wi' 
In which 

AE = B.t.u. work with Clausius cycle per lb. of steam. 

Hi = Actual B.t.u. indicated work per lb. of steam = -^^• 

W = Pounds of steam theoretically needed per i.h.p.-hr. with 

Clausius cycle = 2545 -f- A.E. 
Wi = Pounds of steam actually used per i.h.p.-hr. as found 

by weighing the water used. 

(b) The cylinder efficiencies of steam engines and turbines 
range from 40 per cent to 80 per cent, and in one exceptional case 
88.2 per cent was attained. The reasons for the differences 
occurring between the real cycle and the Clausius, and for the 
losses which they represent, and the methods of reducing these 
losses, will be discussed in the succeeding sections. 

208 



ACTION OF STEAM IN REAL ENGINES. 209 

If the same Clausius cycle is followed by two reciprocating 
steam engines, or by a reciprocating engine and a steam turbine, 
the ratio of the consumptions of steam, or heat, per i.h.p.-hr. of 
the two engines is equal to the inverse ratio of the cylinder 
efficiencies. If the theoretical cycles are not the same, such a 
comparison should not be made. 

(c) It is at times necessary to predict the performance of a 
new engine, or turbine, when operating under certain definite 
conditions. In such cases the B.t.u. of work, A£, done by the 
Clausius cycle, per pound of steam, can be computed from Eqs. 
(188) and (191), or can be obtained from the Mollier diagram in 
the Appendix; then if the proper value of the Cylinder Efficiency 
(/£/) can be found, from data relating to similar engines oper- 
ating under like conditions, the probable number of heat units 
that will be converted into work per pound of steam is, from 
Eq. (228a), 

Hi = AEX lEf, (229) 

and, from Eq. (228b), the probable steam consumption per 
i.h.p.-hr. is 

Wi = 2545 ^ (AE X lEf) (230) 

(d) The Thermal Efficiency on the i.h.p. (TIEf), Section 105 
(g), is the ratio of the indicated work to the heat supplied for 
doing this work; it is therefore a measure of combined efficiency 
of the cycle and of the cylinder with its appurtenances. 

The engine cannot use heat that is of temperature lower than 
that of the exhaust steam T^* and, theoretically at least, the heat 
remaining in the condensate can be returned to the boiler with 
the feed water; hence the heat of the hquid below this lower 
temperature is not chargeable against the engine, when considered 
by itself and not in connection with the power plant as a whole. 
Therefore, 

TTJ7f — ^■^•^''- indicated work per lb. of steam , ' . 

Heat supplied above T2 per lb. of steam 

' . (231b) 



(A(2i - 22) • ' ' ' 

= . ?545 r . 

WdAQ^-q2) ^^^^""^ 

*Proc. Inst. C. E. (British), Vol. CXXXIV; and Trans. A. S. M. E., Vol. XXIV, 
pp. 716 and 755 



2IO HEAT-POWER ENGINEERING 

Where Hi = B.t.u. of actual indicated work per pound of steam 
= 2545 ^ Wi= AE X lEf . ...... (232) 

A(2i =(xr + q + CpD), (233) 

22 = heat of liquid above 32 degrees when at the tem- 
perature T2* of the exhaust steam. 
Wi = Pounds of steam actually used per i.h.p.-hr. as 
found by weighing the water used. 

The value of TIEf varies with the kind of engine and condi- 
tions of operation, and ranges in practice from 5 per cent to 25.05 
per cent, this latter value being the maximum yet recorded. 

In the case of a new engine, the probable performance may be 

computed, if the value of TIEf for similar engines and conditions 

are known, by using the following equations^ derived from Eq. 

(216): w. ^ 2545 - KA(2i - 22) X TIEf I . . (234) 

Hi = (A(2i - 22) X TIEf. (235) 

(e) The Mechanical Efficiency (MEf) of the steam engine 
mechanism varies from 85 to 97 per cent. 

(f) The measure of the combination of the efficiencies of the 
cycle, cylinder, and engine mechanism is the Thermal Effi- 
ciency on the d.h.p. (TDEf), Section 105 (h). The TDEf can 
be computed from Eqs. (219) and (220). Since it is the ratio of 
the B.t.u. of work delivered, to the heat supplied in doing that 
work, 

^°^f - WAW---13 ^'^'^ 

in which Wd is the weight of working substance supplied to the 
engine per d.h.p.-hr., and AQi is the heat per pound as given by 
Eq. (233), and q^ is the heat of the liquid at exhaust tempera- 
ture T2. 

The TDEf is from 85 to 97 per cent of the TIEf, the ratio 
being equal to the mechanical efficiency. 

The probable performance of an engine on the basis of de- 
livered power may be estimated by using the following equations, 

Wd = 2545 -^ KA<2i -52) X TDEf I = Wi -^ MEf (237) 

^""^ Ha=TDEf{AQ^-q,), (238) 

where Hd is the B.t.u. of work delivered per pound of steam. 

* Proc. Inst. C. E. (British), Vol. CXXXIV; and Trans. A. S. M. E., Vol. XXIV, 
pp. 716 and 755. 



ACTION OF STEAM IN REAL ENGINES 2ll 

(g) The measure of the performance of the engine as a whole 
as compared with the ideal engine following the Clausius cycle 
is given by the Overall Efficiency {OEf) . This is the combined 
efficiency of cylinder and mechanism, hence OEf = lEf X MEf 
as in Eq. (221). Since it is the ratio of work actually delivered 
to that which would be delivered by the ideal engine, 

O^f-wf^' ■ ■ ■ ■ ■ (^39) 

in which Wd is the weight of steam actually used per d.h.p.-hr., 
and A£ is work theoretically obtainable per pound of steam fol- 
lowing the Clausius cycle. AE can be computed by using Eqs. 
(188) to (191). 

The overall efficiency of steam engines is from 35 to 78 per 
cent. 

The probable performance of the steam engine, based on the 
delivered output, can be estimated from 

W, = 2545 - (AE X OEf) (240) 

and 

Hd= AEX OEf (241) 

116. Actual Behavior of Steam in an Engine Cylinder, (a) 

The materials with which the steam comes in contact in the 
engines previously considered have been assumed to be perfect 
nonconductors of heat; but materials actually used are good 
heat conductors, and this modifies the behavior of steam in real 
engines. 

(b) The steam on its way from boiler to engine gives up to 
the pipe a part of its heat, which is lost by conduction, radiation, 
and convection. Because of this, the steam arrives at the 
engine with quality or superheat reduced. There is another 
loss due to the drop in pressure necessary to cause the steam 
to flow from the boiler to the engine against resistances due to 
friction of the pipe and inertia of the steam itself.* 

(c) At the engine the steam on its way to the cylinder passes 
through a " Throttle Valve." If this valve is only partly open, 
the steam is " Throttled " or " Wire-drawn," with an accom- 
panying drop in pressure. These changes take place with such 

*This kind of loss will be considered later in the chapter on flow of steam 
through pipes. 



212 



HEAT-POWER ENGINEERING 



great rapidity and within such small space that little heat loss 
to the outside can occur, but as there is an increase in the veloc- 
ity of the steam there is a small amount of heat expended in im- 
parting kinetic energy. This, however, returns as heat when 
the velocity is reduced in the engine. The heat lost while the 
pressure is decreased is so small as to be negligible, hence the 
process may be considered one in which the total associated heat 
remains constant. The throttling increases the quality . (or 
superheat), the value of which can readily be found by follow- 
ing along the proper constant-heat line either on the Mollier 
diagram or on the T(/)-diagram, from the point for the initial 
condition to that for the lower pressure (or temperature). 

A further wire-drawing takes place, with a similar effect on 
the condition of the steam, while the steam passes the more or 
less restricted opening of the admission valve on its way to the 
cylinder. 

(d) When the steam enters the clearance space in the cylinder, 
it comes in contact with surfaces that were cooled during the 
period of exhaust of the preceding cycle. In the resulting inter- 
change of heat, the temperature 
of the clearance walls is raised, 
and ordinarily from lo to 40 
per cent of the steam is con- 
densed. The corresponding de- 
crease in the quality of the 
steam is shown by the inclina- 
tion of the quality curve Xibi in 
Fig. 82. 

As the piston recedes during 
admission {he), an increasing 
amount of the cylinder wall is 
exposed to the entering steam 
and further condensation takes place (as shown by the slope of hiCi) 
until, at the point of cut-ofif, from 20 to 50 per cent of the steam 
has usually been condensed. Next to the heat loss inherent in 
the theoretical cycle, this Initial Condensation, as it is called, 
causes the largest loss that ordinarily occurs in the steam engine 
and is therefore the one most desirable to minimize. 

(e) During admission the pressure is decreased by the wire- 
drawing of the steam while passing the admission valve and 




Fig. 82. 



ACTION OF STEAM IN REAL ENGINES 213 

while flowing through the passages to the cyHnder. This does 
not represent any appreciable loss of heat, however. It improves 
the quality or superheat of the entering steam somewhat and 
may reduce the initial condensation a very slight amount. 
The decrease of pressure by wire-drawing and the effect of con- 
densation during admission are shown by the downward slope 
of the admission line, be. 

(f) After cut-off (c), the condensation continues, until expan- 
sion has reached a point (t) where the temperature of the steam 
equals the mean temperature of the exposed cylinder walls. 
The accompanying change in quality is shown by the curve 
Cih. With further expansion the average quality of steam 
increases; steam is still condensed on the surfaces newly un- 
covered by the continued motion of the piston, but the heat 
thus absorbed by the cooler portion of the cylinder wall is less 
than that given up, to evaporate moisture, by the rest of the 
wall which is at relatively higher temperature. The increase 
in quality is shown by hri. Of course, the condensation during 
expansion is not all due to the influence of the cylinder walls, 
for heat must be used in performing the external work, as was 
shown in Section 114 (b). 

The quality curve Citifi, for the period of expansion, is readily 
obtainable after the saturation curve has been drawn for the 
total weight of mixture in the cylinder; but that part of the 
quality curve which relates to admission (xibiCi) is indeter- 
minate and is therefore shown dotted in the figure. 

(g) Theoretically, expansion should be continued to the 
point d on the back pressure line; therefore, in the actual case 
there is a loss due to incomplete expansion,* measured by the 
area rde. 

During release (re) the steam is dried to some extent by the 
heat that is given up by the cylinder wall to the steam, which 
is now at a low temperature, and also by the heat released from 
the steam itself while decreasing in pressure. 

(h) During exhaust (ek) the confining walls are cooled by 
the outflowing steam, and by the evaporation of the film of 
moisture on the walls. The greater the amount of moisture, 
within limits, the cooler will the walls become and the greater 
will be the amount of steam condensed during admission in the 
*See Section iii. 



214 



HEAT-POWER ENGINEERING 



next stroke. The exhaust pressure, or back pressure, is some- 
what higher than the theoretical because of the resistance to 
steam flow offered by the valve opening and passages, by the 
inertia of the steam itself, and because of the evaporation of 
moisture. 

(i) During compression the quality of the steam is indeter-' 
minate. It is usually assumed, however, that the steam is dry 
at the beginning of compression, and this is accurate enough for 
most practical purposes because of the small weight of steam 
involved. During the first part of compression the steam will 
probably be slightly superheated owing to the reception of heat 
from the hotter walls of the cylinder. If the compression is 
high, the temperature from compression may rise 

r^^^^X above that of the cylinder walls, in which case 

\^_____^ condensation will follow. Further compression 
of the now saturated steam will be at constant 
pressure, and on the PV-diagram the line be- 
comes horizontal, thus forming the " hook " as in Fig. 83.* 

(j) The cycle is further influenced by the leakage of steam 
past the valves and around the piston, which would modify the 
actual diagram. 

(k) The loss of heat from the cylinder walls by radiation, 
conduction, and convection lowers the mean temperature of the 
walls and adds slightly to the condensation. 



Fig. 83. 



117. Diagrammatic Representation of the Heat Interchange 
in the Cylinder, (a) In the PV-diagram, Fig. 84 (a), the point 




C represents the total charge of steam and water in the cylinder, 
considered raised to the initial pressure and in a dry saturated 
condition. CC is an adiabatic expansion line drawn through 

*A somewhat similar hook occurs when there is leakage past the piston or 
valve. 



ACTION OF STEAM IN REAL ENGINES 



215 



this point, and fCC'g is the Clausius diagram which this charge 
should theoretically give. The actual diagram (omitting com- 
pression and clearance) is fbcreg. If through c the adiabatic 
C1C2 is drawn, then fciC2g is the Clausius diagram for the vapor 
actually present at cut-off. Thus the loss of area from initial 
condensation is seen to be ciCC'c2, and that due to wire drawing 
is bcci. That the expansion line from c to t has greater slope 
than CC2 shows that the condensation takes place more rapidly 
than it would with adiabatic expansion. At t the temperature 
of the steam is the same as that of the cylinder walls, and from 
i to r reevaporation takes place, as shown by the expansion line 
being more nearly horizontal than the adiabatic. 

The loss due to early release is shown by the area rde, in which 
rd is an adiabatic line. 

(b) The diagram for the compression of the cushion steam 
is shown separately in Fig. 84 (b) by gkaai; and above it is the 
area aiabf for admission at constant volume. By subtracting 
Fig. 84 {b) from Fig. 84 (a) the net diagram is obtained, as in 
Fig. 84 (c). 

(c) The use of a T^-Diagram to represent the heat inter- 
changes occurring in the cylinder is more or less conventional 
and is only partly correct from the theoretical standpoint. In 




Fig. 85. 

Fig. 85, which is lettered to correspond with Fig. 84, fCC'g is 
the Clausius diagram for the total weight of charge used per 
cycle; fbcreg conventionally represents the actual diagram, neg- 
lecting clearance and compression; and fciC2g is the Clausius 
cycle for the vapor actually present at the time of cut-off. 
The loss of heat to the cylinder wall due to initial condensation 
is given by area below CiC down to the 4>-axis; but as that 
part below C2C' could not be utilized, the net loss of area from 
this cause is CiCC'c2. The wire-drawing loss is represented 



2l6 HEAT-POWER ENGINEERING 

approximately* by the area bcci. That heat is lost to the 
cylinder wall after cut-off is shown by the sloping of the expan- 
sion line ct to the left of the adiabatic CC2, which indicates that 
the quality decreases more rapidly than it would with adiabatic 
expansion. At t condensation ceases; and from / to r reevapo- 
ration takes place, accompanied by an increase in the quality. 
The loss due to early release is represented approximately by the 
area erd. 

(d) The T(^-diagram for compression of the small weight of 
cushion steam is shown in Fig. 85 (b) by the negative area kaaig 
drawn to the same scale as before, except that the width has 
been reduced in proportion to the weight of working substance 
involved. Here it is assumed that the steam is dry at the be- 
ginning of compression, in which case the saturation curve S 
would pass through the point k. The heat lost to the cylinder 
walls during compression is shown by the area under ka, and 
the qualities during compression can be readily determined in 
the usual manner on such diagrams. 

In Fig. 85 (c) the intercepts between a'g and ak are the same 
as those between the similar lines in Fig. 85 (b) ; ab is the line for 
the constant volume during admission (corresponding to ab in 
Fig. 84) , and fbcreg is the same as in Fig. 85 (a) . The area abcrek 
evidently approximately represents the work done during the 
actual cycle. 

(e) Obviously, cr is the only part of the diagram that shows 
the true behavior of all the steam used per cycle ; for, during the 
other parts of the cycle, only a part of the steam is within the 
cylinder. As the T^-diagram is ordinarily used in connection 
with the actual steam engine, it is assumed that if x parts of dry 
steam are present, the associated heat is the same as that of 
all the steam when at quality x, and the state point is located 
on the diagram accordingly. This is fallacious, since x (r -{- q) 
is not the equivalent of (xr-\-q). Thus, the T(/)-diagram is 
correct only for the expansion process (the weight of material 
being constant) ; it is erroneous to use it quantitatively for the 
other processes, but it shows in a general way what interchanges 
occur in these other cases. As the T(/)-diagram is ordinarily 
interpreted, it would be said that while tracing the line from 
6 to c the quality would be increasing, but in this case it is the 

* The reason this is approximate will appear later. 



ACTION OF STEAM IN REAL ENGINES 217 

volume of the vapor that is increasing in the cyHnder, while at 
the same time its quality is usually decreasing. Again, while 
ek is being drawn, the volume of the steam in the cylinder is 
decreasing, and the quality is increasing. 

(f) In the foregoing discussion the upper and lower temper- 
atures were taken as those occurring in the cylinder itself. If 
isothermals corresponding to the boiler and condenser temper- 
atures are drawn on the diagram, the added areas would show 
the losses between the boiler and cylinder and between the 
cylinder and condenser. 

118. Derivation of a T0-Diagram from a PV-Diagram. (a) 
First Method. On the PV-diagram draw the saturation curve 
for the total weight of mixture (w) involved; take numerous 
points around the diagram; and for each get the temperature 
(r), and the ratio (X) of the actual volume to that of dry 
saturated steam as given by the saturation line. Note that 
during expansion X will be the quality, 
while during other parts of the cycle it is 
simply a ratio of volumes. 

Prepare a T<^-chart as in Fig. 86, by 
drawing the water and saturation curves. ' 
This may be done conveniently by using 
absolute temperatures and entropies of 
water and vapor given in the Steam ^jg 86. 

Tables, the entropies being multiplied by w 

before plotting. For each value of T draw the isothermal line TC. 
Then the distance ^C is the entropy of vaporization. Locate 

AB 
the point B on .4 C in such position as to make -r-^ equal to the 

value of X obtained from PV-diagram. The locus of points B 
thus found will be the desired diagram. 

(b) The foregoing applies only to saturated steam. If X 
should be greater than 100 per cent, the temperature (Te) of 
the superheated steam must first be found, and this may be 
done by using Tumlirz's formula in the manner explained in 
Section 114 (c) ; then the corresponding point Bs (Fig. 86) must 
be located in the region of superheat on the pressure line P at 
the temperature elevation Ts. 

(c) If a T0-chart for one pound instead of for (w) pounds 
is constructed like Plate I in the Appendix, it may be used for 



a/^ 




\/Bs 


Jk 


? 


Vr., 


/U> \ 



2l8 



HEAT-POWER ENGINEERING 



the derivation of a T^-diagram by plotting corresponding 
values of T and X directly; and it can be used regardless of 
the weight of steam involved, thus avoiding the construction 
of a new chart for each case. It must be remembered, however, 
that the areas on such diagrams represent the heat for only one 
pound of steam. 

(d) Second Method (Graphical). In this method it is first 
necessary to prepare a Boulvin Chart* such as is shown in 
Fig. 87, in which there are four quadrants with related co- 




Fig. 87. 

ordinates. The first quadrant (I) is for temperature-entropy 
(T^) relationships; the second (II) for temperature-pressure 
(TP); the third (III) for pressure- volume (PV) ; and the fourth 
(IV) for entropy- volume (0V). 

(e) In the PV-quadrant let the saturation curve ss', for the 
weight of steam w, be drawn with any convenient scales for the 
pressures and volumes. Then, in the PT-quadrant, plot a 
curve showing the pressure-temperature relation for saturated 
steam, using the same pressure scale as before and any suitable 
one for absolute temperatures. Next, in the T0-quadrant, 
using the same temperature scale and any convenient one for 
entropy, construct the curves for water and for saturated steam. 
Then for any pressure p, the chart shows that the volume of 
the saturated steam is ps; that the temperature is pz = ot; 

* " Entropy Diagram," by J. Boulvin, published by Spon and Chamberlain. 



ACTION OF STEAM IN REAL ENGINES 219 

that the entropy of the water is tf; and that the entropy of 
vaporization is fS. 

(f) While steam is being generated, the entropy of vaporization 
increases uniformly with the volume of vapor formed. For the 
particular pressure, p, under consideration, this relation may be 
shown in the remaining fourth quadrant (IV) by the straight 
<^V-curve fiS\. This curve is obtained by projecting downward 
from the points / and 5 on the T(^-diagram and by making gfi = 
the volume occupied by the water = w X O.017,* and hSi = ps ^ 
(the volume of w pounds of dry saturated vapor). To complete 
the chart, similar cjAl lines must be drawn for each of the other 
pressures used. 

(g) On this chart the actual PV-diagram can now be drawn in 
the PV-quadrant (III) and from it the corresponding T0-diagram 
can be obtained by simple projection. For example, starting 
with the points u and U (at the pressure p) on the PV-diagram, 
project horizontally to the </)V-curve, fiSi, for that pressure, and 
thence upward' to intersect the corresponding isothermal line at 
-Ml and Ui. The points thus found are on the T^-diagram desired 
and other points can be located in a similar manner. By passing 
curves through the points, the complete diagram is obtained. 

(h) With superheated steam, this construction does not apply, 
and in this case the procedure would be that outlined in (b) of 
this section, 

(i) If a Chart for One Pound of Steam is constructed, it may be 
used for any case regardless of the weight (w) of steam involved. 

Then, however, the volumes to be used on the chart are ( — )th 

of the actual volumes occupied by the steam in the cylinder; and 
the areas represent the work, or heat, for only one pound of steam, 

119. Hirn's Analysis, (a) If certain data, which can readily 
be obtained during an engine test and from the indicator dia- 
gram, are available, the numerical values of the heat interchanges 
between the cylinder walls and the steam can be calculated by 
a method originated by Hirn (in 1876) and formulated later by 
D welshau vers- D ery . 

With such information before him, the engineer can analyze 
the distribution and extent of the losses in each case, and, by 
comparing these results with those obtained with the best engines, 
* This is too small to be scalable, but is shown exaggerated in Fig. 87. 



220 HEAT-POWER ENGINEERING 

he can determine wherein improvements can be made in the 
engine he is considering. 

(b) With the weight of steam per cycle, and the pressure and 
quaHty of steam known at any two points (i and 2) in the cycle, 
the associated heat (Hi and H2) present in the steam at those 
points can be computed. Then (Hi — H2), if positive, is the 
heat surrendered by the steam between the two points; and if 
negative, it is the heat the steam receives. The B.t.u. work (A) 
actually done between points i and 2 of the cycle is shown on the 
indicator diagram by the area below the cycle line between those 
points and extending to the line of absolute zero pressure. Of 
course, if all the heat that is available is converted into work, 
A will equal {Hi — H2). In the actual case, however, there is 
some heat interchange between the cylinder walls and the steam. 
Thus, if A is less than (^1 — H2), the steam has lost heat to the 
cylinder walls equal to the difference; and if A is greater, heat 
has been surrendered by the walls to the steam and has been 
converted into work. 

(c) The data needed for Hirn's analysis are: 

(i) The weight (w/) of " cylinder feed " per cycle and its 
quality (xf) as it enters the cylinder, as determined by test of 
engine. This gives means of computing the heat H/ supplied 
by the entering steam. 

(2) The weight of " cushion steam " (wk) per cycle and its 
quality (xk) at the beginning of compression. 

(3) An average indicator card, with PV-axes, saturation 
curve, and quality curve, as in Fig. 88 (a) and (b). 

(4) The B.t.u. equivalent of work per cycle as determined from 
the areas Aa, Ac, Ar, Ae, and Ak on the diagram. Fig. 88 (c) and (d) . 

(5) The heat (Ki) in the water of condensation, and the heat 
(K2) carried away by the condensing water, supposing a surface 
condenser is used. 

The leakage must be practically zero and is considered such in 
this analysis. Account must also be taken of the fact that 
during the reception of steam at constant pressure, the APu 
quantity is abstracted; thus throughout expansion and com- 
pression the heat in the steam is (xp + q) instead of (xr + q) for 
saturated steam, and is (X + CpD —APtis),* instead of X + CpD, 

*Here Us = (Vs — 0.017) = the increase in volume accompanying tlie forma- 
tion of superheated steam from one pound of water, i.e., it is the increase of volume 
during vaporization and during superheating. 



ACTION OF STEAM IN REAL ENGINES 221 

for superheated steam. This also is true of the steam contained 
in the cyHnder at each point in the cycle, because at some time 
before the point is reached the piston has moved out against 
resistance to make available the necessary volume and the APu 
quantity has thus been utilized. 

(d) During the first part of the cycle, heat {Hf) is supplied 
by the entering steam (cylinder feed) and this is added to the 
heat {Ha) in the cushion steam at the end of compression. 

The heat associated with (" in ") the entering "cylinder feed " 
is, in the case of saturated steam, 

Hf = Wf (xr + q)f, (242) 

and for superheated steam is 

Hf = Wf (X +C,D)f (243) 

At k (Fig. 88) the steam is assumed to have 100 per cent quality, 
as explained in Section 113 (b) ; hence the weight of the cushion 

steam is Wk = ^ , where Vk is the absolute volume at k and Yh is 

the specific volume for the pressure at that point. 




The weight of that part of the cylinder content that is in the 

. . Va 

form of vapor at a is similarly Wa= -^. Hence the quality at a 
is Xa = — ^ and the heat in the steam at this point is 

Wk 

Ha = Wk (Xp + q)a (244) 

Then at the end of admission (point c) the heat in the steam is 

He = (wk + Wf) (xp +q)c (245) 

in which Xc is found from the quality curve (Fig. 88 (&)). 



222 HEAT-POWER ENGINEERING 

The work in B.t.u. per cycle actually done on the piston during 
admission is Aa, as determined from diagram Fig. 88 (c); and 
the heat given up by the steam is ( iJ/ + Ha) — He ; hence the 
heat interchange during admission is 

La = (Ha + Hf) - He- Aa. • . (246) 

A positive result indicates that heat is lost to the cylinder and 
a negative one shows that the steam has received heat from the 
cylinder. The same will be true for the other equations for heat 
interchange that follow. 

The proportion of heat that is interchanged is La -r- {Ha -\- Hf 
— He), and this is a close measure of the proportion of steam 
that is condensed, that is, it is a measure of the " initial conden- 
sation." 

(e) At the beginning of expansion the heat in steam (at c) is 
He from Eq. (245). 

The heat in steam at r is 

Hr = {wk + Wf) (xp + q)r, .... (247) 

in which Xr is obtained from the quality curve in Fig. 88 {h). 

The work in B.t.u. actually done during expansion is deter- 
mined from area Ae on the diagram. 

Then the net heat transfer from steam to cylinder wall during 
expansion is 

Le = {He - Hr)- Ae (248) 

A negative result indicates that the steam receives heat from the 
cylinder wall. 

Note that the loss between cut-off and any other point on the 
expansion line can be computed in a similar manner; thus it is 
possible to determine the interchanges between cut-off and all 
points throughout expansion. 

(f) If the exhaust steam is condensed in a surface condenser, 
the condensate (of temperature 4) per cycle will contain heat 
above 32 degrees, 

Ki = Wf {te — 32°), or more accurately = Wfqe] . (249) 

and the condensing water (of weight Wx per cycle, with initial 
temperature h and discharge temperature td) will take away 
heat, 

K2 = Wx {td — to), or more accurately, = Wx {g_d — qo)- (250) 



ACTION OF STEAM IN REAL ENGINES 223 

Between r and k, the steam for a while does work, as shown 
by Ar on the indicator diagram; afterwards work is done upon 
it, as shown by Ae. At r the heat in the steam is Hr (from 
Eq. (247)), and at k there is left in the steam Hk = Wk{p + g)k, 
since Xk is taken as unity. 

Hence the heat interchange during exhaust is 

Le = iHr- Hk) - {K, + K^) - {Ar " Ae), . (251) 

in which positive and negative results have the same meanings 
as explained in connection with Eq. (246). 

(g) If the steam is exhausted to the atmosphere, the heat 
discharged is indeterminate. An approximation can be made if 
the mean quality of the exhaust steam is known, but it cannot 
be computed accurately because the weight, pressure, and 
quality of steam are variable throughout the exhaust period. 

(h) During compression the change of associated heat is 

{Hk - Ha), 

^"^^^^^ Hk=Wk{p+q)k (252) 

^""^ Ha=Wk{xp+q)a (253) 

The work actually done upon the steam per cycle is shown 
by Ak. Hence the heat interchange during compression is 

Lk= Hk- Ha + Ak, (254) 

in which the sign of Lk has the same meaning as before. 

(i) Ideally, the heat given to the cylinder walls should equal 
that given up by them to the steam. Actually, in the case of an 
ordinary engine, the heat given up is less than that received, 
and this is because of conduction and radiation. Evidently, 
the conduction and radiation loss in B.t.u. per cycle is 

R=La + L, + Lr+Lk. . . . (255) 

(j) If the steam is initially superheated, the analysis would 
be carried through in a manner similar to that just given. If 
the engine is steam- jacketed (Section 129), or is a compound 
engine with reheating receivers (Section 130), account must be 
taken of the heat furnished by the jacket steam. 

120. Experimental Determination of the Actual Performance 
of Steam Engines, (a) The indicated horse power of an engine 
can be determined from the indicator diagram, if the diameter 



224 HEAT-POWER ENGINEERING 

of cylinder, length of stroke, and r.p.m. of the engine are known. 
The delivered horse power can be measured by a Prony brake 
or other form of dynamometer and in other ways which need 
not be considered here. The mechanical efficiency of the 
engine and power lost in engine friction can then be calculated. 
The total amount of steam used per hour may be determined 
by weighing the water pumped to the boiler which supplies the 
engine, making proper allowance for loss or withdrawal of 
working substance between the pump and the engine; or it 
may be found by weighing the condensate, if a surface conden- 
ser is used, and making correction for leakage. The weight of 
steam used per h.p.-hr., or Water Rate, can then be obtained 
as in Section io6. 

(b) If these measurements are made for a range of loads on 
the engine, the resulting data can be used in plotting curves of 
Total Consumption of Steam (TC) and of Rate of Consumption 
(R), as in Fig. 71. These curves show the performance of the 
engine under all conditions of loading, and determine the power 
output at which the engine operates most economically. The 
curve of total consumption is usually nearly straight. If the 
abscissas are d. h.p.-hr., the Y-intercept shows the steam used 
in overcoming the friction of the engine alone. 

(c) If two engines receive steam of the same pressure and 
quality, their relative performance is shown by comparing their 
Water Rates. In other cases the only true measure of econ- 
omy is on the basis of heai used per unit of power, and in order 
to determine the heat in the steam as it enters the engine the 
quality, or superheat, must be known. 

The quality of the steam can be determined by using instru- 
ments which will be described in the next section. 

121. Steam Calorimeters.* (a) The apparatus used to de- 
termine the quality of steam is called a " steam calorimeter." 
There are several kinds of calorimeters, which will be considered 
very briefly. 

The Barrel Calorimeter. 

(b) If into a barrel containing water, of known weight (1^) 
and temperature (/i), a sample of the steam is piped, and con- 

* For more detailed discussion see Carpenter and Diederichs' " Experimental 
Engineering," published by John Wiley & Sons. 



ACTION OF STEAM IN REAL ENGINES 



225 



densed, and if the increase {w) in weight of water and the result- 
ing temperature (^2) are measured simultaneously, there are suf- 
ficient data for determining the quality of the sample of steam, 
provided the steam pressure is known. 
The heat given up by the steam is 

A(2i ^w\xr+q- {ti- 32°)! 
and that received by water is 

^Q2 = w{k-k), 

assuming Cp of the liquid as unity. Evidently AQi = ^Qi, from 
which the quality is found to be 

^_ W{h-k)-w{q + ^2-k) 
wr 

Correction should also be made for conduction 
and radiation losses in accurate work. 

The Separating Calorimeter. 

(c) In using the Separating Calorimeter (Fig. 
89), a sample of steam is first led to the sepa- 
rating chamber C, where the moisture is thrown 
out and collected (the amount w being shown 
by the gauge glass G), then the resulting dry ToWaterCa^v 

steam passes into the jacket J and out through ^^' ^' 

the orifice to a can of water in which it is condensed and its 
weight W determined. Using simultaneous values of w and W, 
the quality evidently is 

W 




The Throttling Calorimeter. 

(d) In this case a sample of wet steam is passed through the 
device shown in Fig. 90, and is superheated by being throttled 
through the valve V while expanding into the cup C, where the 
pressure is low. 

This pressure is usually nearly atmospheric when high-pressure 
steam is being sampled. If the sample of steam is at pressure 
near or below that of the atmosphere, the cup may be connected 
with a condenser to obtain a sufificiently low pressure therein. 

The temperature ta of the superheated steam in this cup C is 



226 



HEAT-POWER ENGINEERING 



measured by the thermometer T; and the degrees of superheat D 
are found by subtracting from 4 the saturation temperature tz 
corresponding to the cup pressure shown by the manometer. 
The expansion through the valve causes the jet of steam to 
acquire a high velocity at that point, hence some of the associated 
heat is converted into kinetic energy. In the cup, the velocity 
of steam is reduced and this kinetic energy is reconverted into 
associated heat. If the velocity in the cup, where the tempera- 
ture ts is measured, is the same as that in the main steam pipe 
(which is usually approximately true), and if there are no radia- 




tion or conduction losses (and these are usually almost negligible), 
the associated heat is the same before and after the steam passes 
the expansion valve. 

Before throttling, the amount of heat per pound is 

AQi = xin + gi ; 
afterward, it is 

A(22 = X2 + Cp (D) = X2 + 0.48* (ts - h). 
Then since 

A<2i = A(22, 
the quality is found to be 

^^ = X2+048*fe-/2)-gi (258) 

* For cup pressures other than atmospheric substitute the proper value of Cp 
for 0.48. 



ACTION OF STEAM IN REAL ENGINES 227 

The Electric Calorimeter. 

(e) In using this calorimeter the sample of wet steam is dried 
by letting it flow over coils of wire which are heated by an elec- 
tric current, the energy input being measured by a wattmeter. 
The watts are gradually increased until a value E is reached at 
which the thermometer in the calorimeter outlet starts to rise, 
which is supposed to show that all moisture has been dried by 
the heat from the coils, by expending an amount of heat corre- 
sponding to E. If the quantity of mixture (w) flowing through 
the calorimeter in a given time is weighed, or otherwise deter- 
mined, the heat (Ji) added to dry one pound of the steam can be 
computed from the electrical input. Then 

r — h , . 

X = —^ (259) 

M 
The Degrees of Superheat. 

(f) This is determined by subtracting the saturation tempera- 
ture, for the existing pressure (as shown by a pressure gauge),. 
from the actual temperature of the steam, as shown by a ther- 
mometer placed in the steam. 

122. Weight of Steam Accounted for by the Indicator 
Diagram, (a) Not only is it possible to draw a theoretical PV- 
diagram for a given weight of steam per cycle, as has already 
been done, but obviously, if a diagram is given and the scale of 
volumes is known, it is possible to determine the theoretical 
weight of steam that the given cycle would use. This not only 
applies to theoretical diagrams, but also to actual ones. The 
theoretical weight of dry steam per actual cycle can be found in 
exactly the same way as for the theoretical cycle. The ratio of 
what is called the " Steam Accounted for by the Diagram," 
" Indicated Steam Consumption," or " Diagram Steam," to the 
steam actually used by the engines is useful in showing the per- 
fection of performance within an engine cylinder. This ratio can 
be easily obtained, and the difference between the weight of dry 
steam actually used and the theoretical is the amount liquefied 
by cylinder condensation. 

In the actual case it is convenient to consider the working sub- 
stance within the cylinder as a mixture of dry steam and water. 
The indicator diagram shows the behavior of the vapor only. 



228 HEAT-POWER ENGINEERING 

(b) Suppose the clearance line and zero-pressure line, that is, 
the PV-axes, have been drawn on an actual diagram, Fig. 91. 

Then let V^ be the volume as scaled 

'C—^Jy I to some point z on the expansion 

c\] line, between cut-off and release* 

[a ^v. and let V2 be the specific volume at 

|\ j?\ the corresponding pressure. Then 

i _> ^,& the total indicated weight of dry 

-i — ^ t~U" vapor in the cylinder at that time is 

•' ' ^ V. 

Fig- 91- Wj = =^. . . (260) 

Similarly, at any point k on the compression line the weight of 
dry " cushion " steam is 

'^^=^, (261) 

in which Vk is the actual volume as scaled to point k and Yk is 
the specific volume for that pressure. 

Subtracting the cushion steam from the total in the cylinder 
gives the indicated cylinder feed (w/) per cycle; thus 

Wf = {W^ - Wk) = y- - ^ (262) 

As the quality changes during expansion and compression, the 
value of w/ will depend on the locations of points z and k. It 
is customary to take z either near the beginning or near the end 
of expansion, and k is usually assumed near the beginning of 
compression. 

(c) Now let yc — clearance volume -^ piston displacement per 

stroke = y in Fig. 91.. 

yz = fraction of stroke completed corresponding 

to any pomt on the diagram 

a = area of piston in square inches. 
pm = m.e.p. 
L = stroke in feet. 
n = number of Cycles per minute. 

Then the piston displacement in cubic feet per stroke isf 



ACTION OF STEAM IN REAL ENGINES 229 

and the volume of vapor when any fraction y^ of the stroke is 
completed is 

Substituting this and a similar value for the volume Vk in 
Eq. (262) gives for the number of pounds of Indicated Cylinder 
Feed, per cycle, 

, _ aL ( y, + ye yk + yc \ . . 

Multiplying this by (60 X n) cycles per hour and dividing by 

— ), gives the number of pounds of steam per i.h.p.-hr., 

33,000/' ^ 

or " Diagram Water Rate," as 

If points z and k are taken at the same pressure level, p, then 
V. = V, = Vp and 

^' = ;Ps7v- ^ ^y^ + y^^ - ^y' + 3'c) i = ^^^ (y^ - y^)- (265) 

If the pressure is taken as that at the end of compression,, 
then yk = o and 

'^^ = ^rf^>^^' (^^^> 

(d) If W = XiX cylinder feed, represents the dry steam 
actually supplied per i.h.p.-hr. and Wd is the indicated water 
rate corresponding to the point z located at the cut-off, the 
" Cylinder Condensation," or weight of steam condensed by 
the cylinder walls and that lost by leakage, is approximately 
{W — Wdi) per i.h.p.-hr.; and the proportion of the whole that is 
condensed, or " Condensation Fraction," is 

CF = {W -Wd)^W. .... (267) 

If the Condensation Fraction, or " Per cent Cylinder Con- 
densation," is known for a certain type of engine under certain 
operating conditions, then, in considering a prospective engine 
of this class, the probable water rate under the same conditions 
can be estimated by dividing the theoretical diagram water rate, 
found from the probable diagram, by (1 — CF). 



CHAPTER XVI. 

METHODS OF DECREASING CYLINDER CONDENSATION. 

123. Condensation and Leakage, (a) It has already been 
shown that the cyHnder condensation causes the largest loss in 
the steam engine, with the exception of that inherent in the 
theoretical cycle. Condensation is evidently dependent on, 
but not necessarily proportional to, (i) the ratio between the 
condensing surface (S), to which the steam is exposed, and the 
volume of steam used per cycle; (2) the temperature differ- 
ence (T) between the entering steam and the surfaces; and (3) 
the time (t) of exposure, which is inversely proportional to the 

number (n) of cycles (i.e., to - j. For computing the probable 
steam consumption many formulas have been proposed in- 
volving functions of S, T, t, or - , and numerical coefficients 

determined from experimental data. Such formulas are suffi- 
ciently accurate for ordinary purposes, when there is no leakage 
past piston and valves.* 

(b) Unfortunately, while it is possible to determine experi- 
mentally whether or not leakage does occur, the amount of 
leakage per cycle cannot be closely evaluated ; thus it is impossible 
to separate the loss due to leakage from that due to condensa- 
tion. Hence cylinder condensation and leakage must be con- 
sidered together. 

Formulas for cylinder condensation should be derived from 
a study of data from engines that are known to have little or no 
leakage. Unfortunately, most of the data available are from 
engines which were not tested for tightness of valves and pistons 
and hence are unsuitable for the purpose. 

124. Size and Proportions of Cylinder, (a) The size of 
cylinder has an important influence on the cylinder condensa- 
tion. It can be shown by computation that large cylinders 

*For formulas and data see Heck's "Steam Engine," and Thurston's "Manual 
of the Steam Engine." 

230 



METHODS OF DECREASING CYLINDER CONDENSATION 231 

have a smaller ratio of surface to volume inclosed than have 
small cylinders of the same proportions. It is therefore to be 
expected that large engines will have less cylinder condensation 
and consequently will give better economy than small ones; 
and that is actually the case. Very small engines may use 
twice as much as, or even more, steam per i.h.p.-hr. than very 
large ones of the same proportions and same conditions of 
operation. 

(b) The amount of surface in the clearance space (including 
that of the steam passages between valves and cylinder) has 
a predominating influence on the amount of cylinder condensa- 
tion that takes place; for, just after admission, the piston is 
moving so slowly that the time of exposure of the steam to these 
surfaces is comparatively long, hence the amount of condensation 
that occurs is large. Probably the greater part of the cylinder 
condensation occurs in the clearance space. The cylinder 
passages and clearance space should therefore be designed to 
present the minimum amount of surface consistent with the 
other considerations involved. 

(c) The cylinder condensation is also dependent on the 
length of stroke of the engine. If long and short cylinders are 
of the same diameter and have their passages and clearance space 
identically the same, and cut-ofT steam at the same per cent of 
stroke, obviously the ratio of clearance surface to the total 
surface exposed per stroke of the engine is smaller in the long- 
stroke engine than in the one with shorter stroke. Neglecting 
the time element, the long-stroke engine should give better 
economy than the short-stroke one; and in general that is the 
case, though this is in part due to the fact that the long-stroke 
engines are usually also larger, have cylinders that are better 
designed, and have better valve gear than those with shorter 
stroke. 

The time element may have an important influence, however; 
for example, due to the fact that most of the condensation 
occurs in the clearance space and because of the shorter time of 
exposure, some of the short-stroke " high-speed " Corliss engines 
give as good or even better economy than the long-stroke low- 
speed Corliss engines. 

(d) In many engines the exhaust steam flows over the outer 
surface of the cylinder wall, on its way to the exhaust pipe. 



232 



HEAT-POWER ENGINEERING 



=ic3 




100 Ji 



Because of the high velocity of flow, this steam carries away 
heat more rapidly than would stagnant air in contact with the 
same surface. This lowers the mean temperature of the cylinder 
walls and increases the cylinder condensation. In the better 
designed engines the exhaust steam is not brought in contact 
with the cylinder walls after it leaves the exhaust valve. 

125. Influence of Point of Cut-off. (a) As most of the 
cylinder condensation occurs in the clearance space, the later 
the cut-ofT (or the greater the vol- 
ume of steam admitted per cycle), 
the less will be the percentage of 
steam condensed, although the 
amount may be greater, (i) The 
percentage of steam not condensed 
is shown in Fig. 92 (a),* by the or- 
dinates, the abscissas being percent- 
age of stroke at cut-off. (2) The 
work theoretically done per pound 
of steam decreases as the cut-off is 
advanced in the stroke (because of 
the reduction of expansion), hence 
the theoretical steam consumption 
per unit of work is greater the later 
the cut-off occurs, as shown by the 
ordinates of the curve in Fig. 92 {h) . 
(3) Evidently, dividing the theo- 
retical water rate per h.p.-hr.. Fig. 
92 (&), by the percentage of steam 
will give the true consumption at the 
water rate," ob- 



f Cutoff 



f, Cutoff 



ji Cutoff 

Fig. 92. 

not condensed, Fig. 92 {a), 

various cut-offs. The values of the actual 

tained in this way, are shown by the lower curve in Fig. 92 (c). 

Similar "water-rate" curves can be drawn by using data 
obtained by direct engine test, in which the water per i.h.p.-hr. 
is measured with engine operating under different loads (i.e., 
different cut-offs). Usually the water rates are plotted with 
respect to power output instead of cut-offs. 

(b) Inspection of the water-rate curve makes it evident that, 

* This is for large four-valve engines having little leakage. See " Engine 
Tests," by G. H. Barrus. 



METHODS OF DECREASING CYLINDER CONDENSATION 233 

to give the best economy, the engine should he operated with cut-of 
corresponding to the lowest point on this curve. 

The most economical cut-off for noncondensing simple slide- 
valve engines is about \ stroke, and for simple Corliss engines 
it is between ^ and \ stroke. In practice these are the cut-offs 
which predominate. 

(c) Usually the " water-rate curve " is more nearly horizontal 
to the right of the lowest point than it is to the left (as in Fig. 92), 
hence it is better to " overload " an engine than to " underload " it. 

126. Compounding of Cylinders, (a) By using earlier cut-off 
the amount of steam used per h.p.-hr. is reduced theoretically 
because of the greater expansion of the steam. But it was seen 
in the case of the simple engine that cylinder condensation 
becomes excessive with very early cut-offs because of the greater 
temperature range and thus defeats the advantage which should 
be gained theoretically. Therefore, to economically use larger 
expansions than are possible with the ordinary simple engine, 
the cylinder condensation must be reduced in some way. It 
was shown in Section 123 that cylinder condensation can be 
reduced by decreasing the amount of cylinder surface (especially 
that of the clearance space) to which the steam is exposed and 
by reducing the temperature range in the cylinder. Both of 
these methods can be combined in the following manner. 

(b) Suppose a small amount of steam is admitted to a small 
cylinder (say with { the piston area of the simple engine) and 
that it is expanded only enough to 
bring the temperature Tr (Fig. 93) 
of the exhaust steam part way to 
that of the simple-engine exhaust 
(say Tr is halfway between 7"i and 
T2 on the temperature scale). Let 
the indicator diagram labelled H.P. 
in Fig. 93 represent this cycle. Then, 
owing to the smaller cylinder surface 
(especially that in the clearance), ' Fig. 93. 

there is very much less initial and 

cylinder condensation in this case than if the same weight of 
steam had been expanded the same amount in the cylinder of 
the large simple engine. 




234 HEAT-POWER ENGINEERING 

Now let the steam exhausted from the small cylinder enter one 
of the same size as that of the simple engine, and let it be further 
expanded in this cylinder until the back pressure of the simple 
engine is reached. The indicated diagram for this case is shown 
by L.P. in Fig. 93. During this expansion the temperature range 
(Tr to Ta) is low, hence cylinder condensation is also small here. 

(c) It is evident that an engine operating in this manner will 
use much less steam per h.p.-hr. than will a simple engine; 
roughly, it uses only about § to f as much. The best economy 
with the simple engine is obtained when the steam is expanded 
in the cylinder to four or five times its initial volume. In an 
arrangement such as has just been described, the expansion 
giving the best results is from 7 to 16 or more, depending upon 
the conditions of operation. 

(d) When an engine with two cylinders is arranged to operate 
in the manner just discussed, it is called a " Compound Engine " 
or " 2X Engine." The small cylinder is named the " high- 
pressure (H.P.) cylinder " and the large one is the " low-pressure 
{L.P.) cylinder.'' 

Other engines are arranged to expand the steam in three steps, 
or stages, using in succession three cylinders that progress in 
size. These are called Triple -Expansion Engines (" 3X "), and 
the cylinders are termed respectively the " high-pressure,'' 
" intermediate-pressure {LP.)," and the ^'low-pressure." Triple- 
expansion engines use considerably less steam per i. h.p.-hr. 
than do the compound engines. 

In the Quadruple-Expansion Engine ("4X"), four cylinders 
are used in succession. They are termed the H.P. cylinder, the 
"first intermediate (I. Pi.), the second intermediate (I.P2.), and the 
L.P. cylinder. Quintuple engines have been made, but their 
number is very small. 

Strictly speaking, the term " Compound Engine " includes all 
multiple -expansion steam engines, but it has become customary 
to apply it only to those with two cylinders. 

Multiple-expansion engines will be discussed more in detail in 
a later chapter. 

A comparison of the performance of simple, compound, and 
triple engines operating under the same conditions is shown * in 

* See report of test, Carpenter, Trans. A. S. M. E., Vol. XVI. Also Thurston, 
A. S. M. E., XVIII. 



METHODS OF DECREASING CYLINDER CONDENSATION 2 



35 



Fig. 94. The triple-expansion Corliss engine in the laboratories 
of Sibley College was tested with high-pressure cylinder operat- 
ing alone as a simple engine, then with the high and intermediate 
cyHnders acting as a compound engine, and finally with all three 
cylinders as a triple-expansion engine. The results are shown in 











"SIBLEY" 

CORLISS ENGINE 

9ri6;'24"x 36" 










VACUUM 10.8 LBS. AB3. 
WITHOUT JACKETS. 


> 


g^ 










y^ 


^ 









Compo 


undj^ 


U^ 


jriple 


' 






























) 1 


1 


5 2) 


S 


5 3 


2 


5 40 



Ratio of Expansion 

Fig. 94. 



this figure. Larger engines and those with jacketing, super- 
heating, etc., would give better results, but this figure shows the 
relative value of using the different expansions. 

(e) Hirn's Analysis can be applied to the multiple-expansion 
engine, each cylinder being considered independently. The data 
needed for such an analysis (in addition to those required in the 
case of a simple engine) include the quality and pressure of the 
steam entering and leaving each cylinder, the weight of con- 
densate "trapped off" from each receiver and the weight and 
condition of the steam condensed in the reheating coils of the 
receiver, if such are used. It is then possible to compute the heat 
in the steam entering and leaving each cylinder 4nd each receiver. 
Thus besides being able to analyze the heat interchanges and 
losses of each cylinder considered separately, the same thing 
can also be done for each receiver, and for the engine as a whole. 

127. Gain Due to Condensing the Exhaust Steam. If an 

engine when operating " noncondensing " (i.e., exhausting to the 



236 HEAT-POWER ENGINEERING 

atmosphere) gives the indicator diagram shown by the full lines 

in Fig. 95, with mean effective pressure equal to pm, then, if the 

back pressure line is lowered (as shown dotted) an amount equal 

to pk pounds, the area of the indicator dia- 

^....,^^ gram will be increased without any theoretical 

N. change in the amount of steam used per cycle ; 

. ^^--^ the mean effective pressure will be increased 

l^^ A to pmk = {pm + pk) ; the ratio of the power of 

\ 1 ^j^g engine to its value when operating noncon- 

• densing is (pm + pk) -^ pm, and there is no 

Fig. 95. additional expenditure of heat in forming the 

steam used. 
By condensing the exhaust steam in a " condenser " (which, 
being supplied constantly with cold water, acts as a " cold 
body " in maintaining a low temperature), the pressure of the 
exhaust steam can be reduced, — and its value will be that 
corresponding to the condenser temperature. The reduction 
in pressure below atmospheric may be from 10 to 14 pounds, or 
even more. 

Evidently, in developing the same power, a " condensing 
engine " would be much smaller than one operating noncondens- 
ing, other things being equal. However, owing to the additional 
cost, operating expense, increased cylinder condensation, and 
attention involved with a condensing outfit, it is seldom used 
with simple engines. Multiple-expansion engines, however, are 
more commonly operated condensing than not. 

128. Effect of Superheated Steam, (a) The cooling of the 
cylinder walls during exhaust is largely due to their surrender of 
the heat used in evaporating the moisture on their surfaces. As 
the latent heat of vaporization corresponding to the exhaust pres- 
sure is very large, roughly 1000 B.t.u. per pound, the evaporation 
of a small amount of water results in a very considerable reduc- 
tion of the mean temperature of the cylinder walls and conse- 
quently in an increase in the cylinder condensation when the 
steam is admitted. 

When superheated steam is used there is less moisture in the 
exhaust steam, and partly because of this, partly because of the 
slow rate of heat transfer between superheated steam and metal, 
and partly because the incoming superheated steam can give 



METHODS OF DECREASING CYLINDER CONDENSATION 237 

Up heat without condensing, the cyHnder condensation is reduced, 
and the economy of the engine is improved. Thus by sacri- 
ficing superheat to heat the cylinder walls, less heat is required 
at the boiler for evaporating the water and for superheating 
the steam used. It is even possible to superheat sufficiently 
high to prevent all initial condensation. In general, however, 
it seems probable that superheat should not be so high that the 
exhaust steam is superheated; although there is some doubt as 
to this, for one engine test showed better results with exhaust 
slightly superheated than when just dry.* 

In experiments by Ripper f on a small steam engine, it was 
found that 7^° F. of superheat would prevent one per cent of 
cylinder condensation. The specific heat of superheated steam 
under the test conditions is about 0.53, hence the B.t.u. used 
in preventing one per cent of condensation was (7^^ X 0.53) = 4.0 
per pound of steam. For larger engines and other conditions 
from 15° to 25° F. and from 8 B.t.u. to 12 B.t.u. per pound are 
used per percent of saving of condensation.! 

(b) The saving effected by superheating can best be shown 
by an example: 

Let the pressure of steam used by an engine be 135 pounds 
absolute, for which the latent heat is 870 B.t.u. Then, if it is 
assumed that 8 B.t.u. superheat will effect a reduction of one 
per cent in the cylinder condensation, it will save (870 X O.oi) 
= 8.7 B.t.u. that would otherwise be wasted by cylinder con- 
densation; thus the saving is 1.09 times the expenditure. 

If the cylinder condensation is 30 per cent, it could be entirely 
eliminated if (8 X 30) = 240 B.t.u. superheat were added per 
pound of steam. Using 0.52 as the specific heat of superheat, 
the temperature increase would be 240 -^ 0.52 = 461° F. to 
effect this result. (Note that this is a much higher degree of 
superheat than is commonly employed.) 

Assume that the boiler furnishes 1000 B.t.u. of heat for each 
pound of steam generated and that 30 pounds of steam (or 
30,000 B.t.u.) are furnished per i.h.p.-hr. Then, since the 
assumed condensation is 30 per cent, the diagram water rate is 

* Carpenter, Trans. A. S. M. E., Vol. XXVIII. 

t Superheated Steam Engine Trials, Proc. Inst. C. E. (London), Vol. CXXVIII. 
tFor data and references see Kent's " Pocket Book " and Gebhardt's " Steam. 
Power Plant Engineering," both pubhshed by Wiley & Sons. 



238 HEAT-POWER ENGINEERING 

(30 X 0.70) = 21 pounds of steam per i.h.p.-hr. If the steam 
is sufficiently superheated to ehminate all cylinder condensation, 
it will furnish (looo + 240) B.t.u. per pound; or 21 X 1240 
= 26,040 B.t.u. will be furnished per i.h.p.-hr. Then the 

economy of the engine is improved in the ratio f^-^ ) =11=; 

V26,040/ ^' 

while the water rates are in the ratio (|^) = 1.43. Thus it is 
seen that the reduction of water rate is not an accurate measure of 
the saving effected in the heat used. This example is intended 
only to show in a very general way the effect of superheat. 
The numerical quantities for other cases may be very different 
from those used here. 

(c) The saving to be expected by superheating is dependent 
^pon the amount of cylinder condensation that would occur in 
:the same engine if no superheat is used. Evidently the greater 
this condensation, the larger is the saving possible. Ordinarily 
the steam consumption is reduced about 6 per cent with 50° F. 
and about 9 per cent with 100° F. superheat. A reduction of 
15 per cent is frequent and as much as 40 per cent has been 
attained. 

(d) It is found that with high temperatures of superheat 
there is difficulty from warping of cylinder and valves and from 
failure of lubricants unless they are of the highest grade. A 
total temperature of 500° F. is about as high as can be used to 
advantage in ordinary steam engines. Cylinders and valves for 
higher temperatures should be specially designed for the service. 
Above 750° F. there is difficulty in finding materials that will 
endure the temperature for long periods of time. 

129. Use of Steam Jackets, (a) Some cylinders are so 
designed as to be surrounded by " live " steam (usually at 
high and constant temperature). Such cylinders are said to 
be " steam-jacketed." Their walls are maintained at higher 
mean temperature and have less temperature fluctuation than 
in the ordinary cylinder, consequently there is less cylinder 
condensation. The heat received by the cylinder wall from 
the " jacket steam " is the latent heat freed by the condensa- 
tion of a portion of this steam. If the jacket steam is at the 
same temperature as the steam entering the cylinder, the mean 
temperature of the walls will be but little below that of the 
entering steam, hence the condensation will be small. 



METHODS OF DECREASING CYLINDER CONDENSATION 239 

At first it may appear that the weight of cylinder condensa- 
tion thus avoided cannot be more than the steam simultaneously 
condensed in the jacket, in cases where the condition of the 
steam entering both the cylinder and the jacket is the same. 
Because of this, and because the jacket has radiating surface 
which is larger, and which is maintained at a higher mean 
temperature, than in the case of the ordinary cylinder, it would 
seem that no advantage is possible from the use of a steam 
jacket. 

(b) That the steam jacket is beneficial is largely due to the 
fact that, with its use, the amount of moisture evaporated from 
the inner walls of the cylinder during exhaust is greatly reduced, 
thus less heat is abstracted from these walls by the exhaust 
steam and less steam is used in the cylinder. It has been seen 
that one pound of moisture evaporated from the cylinder walls 
carries away roughly 1000 B.t.u. from which there is no return. 
In the case of the jacket, however, the condensate formed in 
the jacket can be returned directly to the boiler, and, as it is at 
boiler pressure and temperature, it will carry back from 250 to 
300 B.t.u. per pound. Thus the net result with the steam 
jacket may be a gain in economy. 

In considering the performance of a jacketed engine the heat 
supplied to the jacket steam must be considered and the water 
rate must be modified accordingly. If the weight of steam 
condensed in the jacket per h.p.-hr. is Wj, the heat used per 
h.p.-hr. by the jacket is Wff, and if (A(2i — gn) is the heat 
added per pound of steam supplied to the cylinder, then the 
true water rate, supposing the jacket condensate is returned 
to the boiler without loss of heat, is 

«--«-'+ !(A^S ^^'^^ 

in which Wc is the weight of steam delivered to the cylinder 
per h.p.-hr. 

(c) As most of the cylinder condensation occurs in the clear- 
ance space, this is the most important part of the cylinder to 
jacket. It is usually only on large engines, however, that the 
cylinder heads are jacketed, in addition to the cylindrical walls. 
It would be desirable to jacket the piston, that is, fill it with 
steam, but practical difihculties prevent this. As there is prob- 



240 HEAT-POWER ENGINEERING 

ably no advantage from having the exhaust steam superheated, 
the temperature of the jacket steam should usually not be much 
higher than that of the steam entering the cylinder. This applies 
especially in the case of the low-pressure cylinders in multiple- 
expansion engines. 

(d) Steam jackets are not always sources of heat economy. 
There may be a net loss (i) if they are used with superheated 
steam, (2) if the cylinder condensation is so small that the jacket- 
ing results in superheating the exhaust steam, and (3) if their 
condensate is not returned to the boiler with little loss of heat. 
They apparently give smaller returns on large engines than on 
small ones. 

The gain in economy is from 30 per cent down to a negative 
quantity. Many engineers are skeptical as to their advantage, 
as the data from various engine tests are somewhat contradictory, 
and as somewhat greater expense is involved in supplying the 
jacket equipment. 

130. Reheating Receivers, (a) In multiple-expansion engines, 
it is sometimes the practice to place coils of pipe, containing 
" live " steam, in the " receivers " through which the steam 
passes on its way from one cylinder to the next. As the steam 
in the coils is at relatively high temperature, it superheats (or 
reheats) the receiver steam, provided the moisture has been 
properly separated from this latter. 

The presence of moisture in the working substance defeats 
the purpose of the reheating receiver. This moisture should be 
removed before the steam reaches the reheating coils, for it can 
be evaporated to better advantage in the boiler. 

(b) The action of the reheating coils is similar to that of the 
steam jacket; and the heat surrendered by the condensation of 
steam in the coils of pipe is to be charged against the engine. 

131. Other Methods of Reducing Cylinder Condensation. 

(a) Cylinders are always " lagged " with some nonconducting 
material such as asbestos, mineral wool, magnesia, etc., to reduce 
the radiation. Some small compound " Lokomobile "* engines, 
which have phenomenal economy, are so arranged that the cylin- 
ders are surrounded by the furnace gases as they pass to the stack. 
*Herr E. Josse in Zeitschrift des Vereins deutscher Ingenieure, Sept. 12, 1908. 
Also see report of test of a Wolf engine, (London) Engineering, Oct. 8, 1909. 



METHODS OF DECREASING CYLINDER CONDENSATION 241 

(b) It is of course evident that the higher the rotative speed, 
(or the greater the frequency of cycles), the less will be the 
cylinder condensation, because the entering steam is exposed a 
shorter time to the cylinder walls. For example the high-speed 
Corliss engines use less steam than the low-speed engines of 
that type, under the same conditions. There are practical con- 
siderations, however, which place limits on the speeds of rotation 
that can be used. 

(c) It has been seen that theoretically the larger the temperature 
range in the cylinder, the greater is the cycle efficiency. In the 
actual engine these greater temperature ranges may be obtained 
by using higher pressures, and it has been shown by experi- 
ments* that, within limits, there is an increase in economy 
accompanying their use, even though the cylinder condensation 
is also increased somewhat. 

The gauge pressures (lbs. sq. in.) usual in practice are about 
as follows: 

Usual Gauge Pressures. Table IV. 

Simple engines 80 to 125 

Compound high-speed engines .... 100 to 170 

Compound low-speed engines . . . . 125 to 200 

Triple- and quadruple-expansion engines . 125 to 225 

(d) It has already been shown that the heat economy of the 
steam engine can be improved by approximating the Regenera- 
tive cycle (Section 109). It can also be bettered by selecting the 
proper compression and the best pressure drop at release, and 
by reduction of wire-drawing through the throttle valve, the 
admission and exhaust valves, and the cylinder passages. In 
some cases, however, the throttling of the steam has been bene- 
ficial, probably because the steam at the reduced pressure is 
superheated a little by the process. 

(e) By the use of a Binary Engine it is possible to use some 
of the heat in the exhaust steam to vaporize a second and more 
volatile fluid (such as sulphur dioxide) and to use the resulting 
vapor in another cylinder from which it is exhausted to a con- 
denser. In this way a considerable increase in power can be 

*Gebhardt's "Steam Power Plant Engineering," p. 286, published by John 
Wiley & Sons. 



242 



HEAT-POWER ENGINEERING 



obtained with the same amount of heat furnished, but at extra 
expense for equipment, attention, etc.* 

(f) If the arrangement of engine is such that as the piston 
moves it uncovers new portions of the cyHnder wall which are 
at temperatures equal to that which the steam has reached by 
its expansion, the condensation will be less than in the usual case, 
in which the steam is brought in contact with walls the whole 
of which have been exposed, during a considerable period of 
time, to the temperature of the exhaust steam. Fig. 96 shows 




Fig. 96. — Unidirectional-Flow Engine. 

diagrammatically the " Straight-Flow " or " Unidirectional- 
Flow " engine which has recently been introduced and which 
operates on the principle just mentioned. Steam is admitted 
by the Inlet Valve at the end and is discharged at the middle of 
the cylinder, when the piston uncovers the Exhaust Ports. As the 
piston moves from the beginning of its stroke the newly exposed 
portions of the cylinder wall tend to assume the temperature 
of the steam with which it is brought into contact; thus there 
is a gradation of wall temperature from the inlet valve to the 
exhaust ports. During compression, which comprises practi- 
cally the whole of the return stroke, the temperature of the 
steam is raised as the process progresses, and as the volume 
becomes less the steam is in contact with decreasing surface 
with increasing mean temperature. 

As the expansion proceeds, the steam in contact with the 
steam- jacketed cylinder head becomes superheated and that in 

*See Peabody's "Thermodynamics," p. 280, published by John Wiley & Sons 



METHODS OF DECREASING CYLINDER CONDENSATION 243 

contact with the piston face is the coldest and contains the most 
moisture. When release occurs the wettest steam is exhausted 
and there is little chance for reevaporation of moisture on the 
cylinder walls. Exhaust closure entraps the hottest vapor, 
which, when compressed, attains very high temperature and 
improves the quality of, or superheats, the entering steam. 

Engines operating in this manner have given remarkably 
good economies, even equalling those obtained with multiple- 
expansion engines. As great a ratio of expansion is used in the 
single-cylinder as is employed in the multiple-expansion engine. 

(g) When the heat in all the steam exhausted by the engine 
can be used in drying kilns, in heating systems for houses and 
factories in winter, or for other purposes, the engine economy 
is not important, for the heat not utilized by the engine is not 
wasted. Radiation, conduction, and mechanical friction are 
always losses, except in cold weather, when they may furnish 
the proper amount of heat to maintain the right temperature in 
the engine room; therefore at such times they are not wastes. 



CHAPTER XVII. 

STEAM ENGINES. 

132. Steam-Engine Parts, (a) Fig. 97 shows diagrammatically 
one of the simplest forms of double-acting steam engine. The 
various parts of- the engine are generally grouped as follows : 

(i) Stationary parts, — which include the cylinder, cylinder 
heads (bonnets), steam-chest cover, stuffing boxes, engine frame, 
outer bearing, and subbase, if used. 

(2) Rotating parts, — consisting of the shaft, crank (disk), fly- 
wheel, and eccentric. 

(3) Reciprocating parts, — the piston, piston rod, crosshead, 
and connecting rod. 

(4) Valve gear, — valve, valve stem (rod), valve-rod guide (or 
rocker arm), eccentric rod, eccentric strap, and eccentric sheave 
(or " eccentric "). 

(b) The steadiness of the rotative speed of the engine during 
the revolution, that is, during the completion of one cycle on 
each side of the piston, is controlled by the flywheel. Flywheels 
will be considered in a later chapter. The number of revolutions, 
or number of cycles, per minute — which is usually called the 
engine "speed" — is controlled by the self-acting governor, 
which in Fig. 97 is of the " throttling," fly-ball type. 

The starting and stopping of the engine is controlled by the 
hand-operated throttle valve which, in special cases, may also 
be used to regulate the operation of the engine. 

(c) Engines usually have the following fittings: drain cocks 
for cylinder and steam chest; cocks for attaching indicators; 
lubricating devices for bearings, guides, and cylinders; and shields 
to collect oil thrown by the crank, the connecting rod, and the 
eccentric. 

(d) Engines are mounted on masonry or concrete foundations 
sufhciently massive to prevent noticeable vibration being induced 
in the surroundings. They are fastened to the foundation by 
" anchor," or " foundation," bolts. 

244 



STEAM ENGINES 



245 




Fig. 97. 



133. Classification and Types of Steam Engines, (a) Owing 
to the great variety of designs and to the diversity of uses to 
which steam engines are put, it is impossible to give any one 
classification that would be satisfactory in all cases. The usual 
commercial types of stationary engines are often classified in 
three groups, — "high-speed," "medium-speed," and "low-speed" 
engines. By " speed " is meant the rotative speed, when used 
in this connection. 

(b) High-Speed Engines are those which have high rotative 
speeds accompanied by strokes which are very short when com- 
pared to the diameter of the cylinder, the piston speed being 
generally in the neighborhood of 600 feet per minute.* The 

* The "piston speed" is the number of feet the piston travels per minute. 
Thus, if L is the stroke in feet and n is the r.p.m., the piston speed is V = 2 Ln, 
since the piston makes two strokes per r.p.m. 



246 



HEAT-POWER ENGINEERING 



stroke is usually about equal to the diameter of the cylinder. 
These engines almost always have a single " balanced " valve 
and a shaft governor. They are often called " short-stroke 
engines," and are designed to occupy the smallest space, have 
the least weight, and "direct connect" to the smallest dynamo, 
for a given power, of any of the stationary commercial types. 
This class includes only engines of comparatively small power, 
the cylinders usually not being made larger than 20 inches in 
diameter. Fig. 98 shows a center-crank engine of this type. 




Fig. 98. — Center-Crank Engine with Inertia Type of Governor. (The engine 
is mounted on a cast-iron subbase.) 



(c) Low-Speed Engines have long strokes (from 2 to 4 times 
the diameter of the cylinder) and usually operate at less than 120 
r.p.m., the speed being limited by the valve gear, the action of 
which becomes unreliable at higher speeds. This class includes 
engines having the " Corliss " and other types of " trip cut-off 
gear." The governor is usually of the " fly-ball " type. An 
engine of this kind is illustrated in Fig. 99. 

(d) Medium-Speed Engines have rotative speeds and strokes 
intermediate between the foregoing. Positively driven multiple 
valves are generally used. The cut-ofif is positive and is often 
effected by a separate valve. The governor is nearly always of 
the " shaft type." The piston speed is around 600 feet per 
minute, being higher on the larger engines. The engine shown 
in Fig. 100 is of this type. 



STEAM ENGINES 



247 




Fig. 99. — Low-Speed Engine with Corliss Valve Gear. Direct connected to an 
electric generator. 




Fig. 100. — Medium-Speed Engine — Shaft Governor — Positive Cut-oiT. 



The medium- and low-speed engines are usually of larger 
power than the high-speed. 

There is no sharp dividing line between these different types 
of engines, and it is sometimes difhcult to decide in which class 
an engine belongs. 

(e) Vertical Engines (Fig. loi) occupy less floor space, have 
smaller foundations, have less cylinder wear, and have slightly 
greater mechanical efficiency, than do horizontal engines. When 



248 



HEAT-POWER ENGINEERING 



large, they are more difficult to erect, and caring for them in- 
volves more effort, as certain parts are reached only by ladders. 





Fig. loi. — Vertical Corliss 
Engine. 



Fig. I02. — Vertical Twin-Cylinder, 
Single-Acting Engine. 



In some special instances engines have been constructed with 
axis inclined with the horizontal. 

(f) Single-Acting Engines (Fig. 102) give half as much power 
as do double-acting engines with the same diameter and stroke 
of piston, consequently a larger engine is required for a given 
output. They use pistons of the bucket, or trunk, type, and 
have no piston rod, therefore they are shorter than double-acting 
engines. 

(g) Reciprocating Engines are so called because they have 
pistons that reciprocate within the cylinder. They are the type 

that is most common, although engines with 
rotary piston would apparently be more de- 
sirable. Many unsuccessful attempts have 
been made to devise an engine of the latter 
form. The difficulty lies in the production 
of a machine that is economical in the use 
of steam after the parts have become worn. 
Prior to 1902 there were issued over 2000 
patents on Rotary Engines, and none have yet been able to com- 
pete with the reciprocating engine as regards steam economy. 




T 



X 



Fig. 103. — Rotary 
Engine. 



STEAM ENGINES 



249 



In some instances, where small size is more important than oper- 
ating cost, they may be used to advantage. Fig. 103 shows one 
of the simplest engines of this type. 

In some instances Oscillating Engines, such as that shown in 
Fig. 104, have been used. The connecting rod and crosshead 
are dispensed with and the shaft is thereby 
brought closer to the cylinder. Steam is 
admitted through one trunnion and ex- 
hausted through the other. This causes a 
side thrust, for which proper provision must 
be made. When the cylinder reaches its 
extreme position, its inertia causes great 
pressure to exist between the stuffing box 
and the piston rod, and these parts must be 
designed to properly resist this force. 

(h) Fig. 105 shows two horizontal "side- 
crank engines." Engines of this type have 
the disadvantage of having a separate 
outer bearing which must be aligned with the main bearing. 
They possess the advantage that there are only two bearings to 




Fig. 104. — Oscillating 
Engine. 




Fig. 105." 



Side-Crank Engine — Right Hand and Left Hand — Running Over 
and Running Under. 



be kept in alignment even when the engine is direct-connected 
to an electric generator, as in Fig. 99. 

A horizontal side-crank engine is said to be right-hand in 
arrangement when an observer, standing at the end of the 




250 HEAT-POWER ENGINEERING 

cylinder (at 5 in Fig. 105) and facing the crank, finds the valve 
gear and governor parts are to his right; otherwise the engine is 
" left-hand." 

A horizontal engine is said to be running over if the crank pin 
is receding from the cylinder when the crank is above the hori- 
zontal center line of the engine; otherwise it "runs under" (see 
Fig. 105). If a double-acting engine " runs over " the crosshead 
will exert downward pressure on the guides during both strokes; 
hence engines are usually operated in this manner. 

(i) Fig. 106 shows a Center-Crank Engine. In this type the 
crank is located between the two main bearings, BB, and the 
belt- and flywheels are overhung. If 
small, these engines may be shipped 
assembled, ready to be mounted on their 
foundations. If direct-connected to an 
-, , , „ , ., I , iii ii i ii electric generator, this latter is substi- 
lilll' ! i ilill tuted for the belt wheel and an out- 
Fig. 106.— Center-Crank board bearing is added. There are 
Engine. ^j^^^^ three bearings to be kept in line, 

which is a disadvantage, as very accurate adjustment of bearings 
is required. 

(j) In some engines the crank case and crosshead-guide 
chamber are inclosed so as to be dustproof and prevent the 
throwing and waste of oil (see Figs. 102 and 109). 

Some inclosed engines are arranged to be self-oiling as regards 
the crosshead, connecting rod, and main bearing. In these cases 
oil is maintained at such a level in the bottom of the crank case 
that the crank disk dips into it, and while rotating throws the 
oil into the crosshead and into collecting pockets from which it 
is fed to the bearings. The oil then automatically drains back 
to the crank case and is used repeatedly without being purified. 

Other inclosed engines are provided with forced or gravity 
oil-feeding systems, in which the lubricant is filtered each time 
before reusing. 

(k) Compound engines have their cylinders arranged in many 
different ways. 

If the two pistons are on the same piston rod, as in Fig. 107, 
the engine is called a Tandem Compound. Such an engine occu- 
pies no greater width than a simple engine of the same power 
and type, but has greater length. A vertical engine of this type 



STEAM ENGINES 



251 



("steeple compound") occupies the same floor space as the 
equivalent simple engine. 

Either the high- or low-pressure cylinder may be placed next 
to the frame. 




Fig. 107. — Tandem-Compound Cylinders. 




Fig. 108. — Cross-Compound Engine. 

If the cylinders are side by side, as in Fig. 108, the engine is 
called a Cross Compound. This engine occupies greater width 
than the tandem compound, but its length is about the same as 
that of the simple engine. As it has two frames, and as other 



252 



HEAT-POWER ENGINEERING 



parts are duplicated, it is more expensive than the tandem; but 
because the cranks may be set at right angles it is possible to 
obtain greater uniformity of turning effort than with simple or 
tandem engines, and therefore a smaller flywheel can be used. 

In some cases, with this arrangement of cylinders the cranks 
are placed diametrically opposite (i8o degrees apart), but the 
turning effort is then about as variable as with the single-crank 
engine. 

When the cylinders are immediately adjacent to each other, as 
in Fig. 109, and have their piston rods attached to the same cross- 
head, with single connecting rod and crank, the engine is usually 




Fig. 109. — Duplex- Compound Engine. 



called a Duplex Compound. The engine occupies the same 
amount of space and has the same crank effort as a simple engine. 

The arrangement of engine known as the Angle Compound, 
shown in Fig. no, occupies the same floor space as a simple engine, 
has the uniformity of crank effort obtained with cranks at 90 
degrees (for in this case connecting rods are at 90 degrees and are 
attached to the same crank pin), and is easily counterbalanced. 

In triple- and quadruple-expansion engines the cylinders are 
arranged in various ways and, looking at the end of the shaft, 
there may be various sequences with which the cranks pass a 
given point. The arrangement of cylinders and the sequence 
and angle between cranks have a predominating influence on 
the counterbalancing of such engines, as will be seen later when 
the subject of counterbalancing is discussed. 

(1) Engines are used for a great variety of purposes, and are 
often referred to by their use; thus there are marine engines 
(Fig. in), hoisting engines, pumping engines, rolling-mill 
engines, air-compressor engines, steam-hammer engines, etc. 



STEAM ENGINES 



253 




Fig. no. — Angle-Compound Engine. 




Fig. III. — Vertical Triple-Expansion Marine Engine — Arrangement. 



254 HEAT-POWER ENGINEERING 

Engines are also classified as stationary, portable, semi- 
portable, mobile (marine, locomotive, traction, road roller, and 
automobile engines). 

The uses to which some engines are put require that they be 
capable of being reversed by hand. This is true of marine 
engines, some rolling-mill engines, hoisting engines, traction 
engines, etc. Such engines are called "reversing engines" and 
have special valve gears, either of the " link " or " radial " types, 
which will be discussed later. 



CHAPTER XVIII. 

STEAM-ENGINE GOVERNORS. 

134. Governing, (a) The term " governing " is applied to 
the adjusting of the power output or speed of an engine, or both 
of these, to fit the variable demand. 

(b) An engine may be governed in four ways: It may be 
(i) " hand-governed," as in the case of automobile, marine, and 
locomotive engines; (2) "mechanically regulated" by a "gov- 
ernor " that acts automatically, as in the usual stationary en- 
gine; (3) " resistance governed," its operation being controlled 
directly by the external resistance; or (4) governed by any com- 
bination of these methods. 

(c) The ordinary stationary engine is usually mechanically 
regulated to maintain approximately constant speed of rota- 
tion at all loads. An engine ope/ating uniformly will develop 
indicated power just sufficient to overcome the friction losses and 
meet the external demand for power. Should a decrease in the 
external load occur, it would result in an excess of indicated power, 
causing an acceleration of the moving parts of the engine, which 
would continue until the mechanism ruptured under the induced 
stresses, unless a governor should come into action to prevent. 
On the other hand, an increase in load would stop the engine 
unless the indicated power were increased proportionately. 

Thus, to maintain constant speed, a " governor " must auto- 
matically adjust the indicated power to balance the friction and 
external load at all times. Exact uniformity of speed is impos- 
sible, as a change in speed is necessary to cause a governor to act. 
This change, however, may be made so small as to be negligible 
in most cases. 

(d) Resistance governing is exemplified by an engine directly 
driving a pump which discharges fluid into a closed reservoir or 
system of piping. The pump will raise the fluid pressure in the 
system to the limit of the engine's capacity, when the engine 
will become ineffective. Should fluid then be withdrawn from 

255 



256 



HEAT-POWER ENGINEERING 



the system, the drop in pressure will cause the engine to start 
again and to continue running until the pressure once more 
reaches the limiting value. To prevent the engine from over- 
speeding in case of sudden withdrawal of fluid, or rupture of 
pipe, a " mechanical governor " or " safety stop " is usually pro- 
vided, so adjusted as to automatically come into operation before 
the safe speed is exceeded. The limit of fluid pressure is also 
generally made adjustable by hand. 

135. Governing of Steam Engines, (a) The adjusting of the 
power developed within the cylinder to meet the external de- 
mand on the engine is usually accomplished in the case of the 
steam engine either by throttling the steam supplied the cylinder, 
or by changing the point in the stroke at which cut-off occurs. A 
combination of both of these methods is possible but is rarely 
used. 

(b) When the engine is governed by throttling, the cut-off is 
fixed by the maximum power which the engine is to develop with 
steam at the maximum pressure. To obtain less power, the 
steam is throttled, thus giving lower admission pressure. Fig. 
112 shows ideal indicator diagrams for such case. 





Fig. 



-Throttle Governing. 



Fig. 113. — Cut-off Governing. 



(c) When governed by changing the cut-off, the admission 
pressure is constant, and the amount of cylinder feed is varied, 
as shown by the ideal diagrams in Fig. 113. 

136. Governors, (a) In most cases the demand is for power 
at constant rotative speed, and the governing device should there- 
fore govern " isochronously." Unfortunately, however, govern- 
ing devices are driven by the engine and operate on a simple 
mechanical principle which requires a change in speed to make 
them act. They are also connected to throttling or cut-off 
devices, each of which must have a different position, or phase 
relation, for each load. Hence the governors must change posi- 



STEAM-ENGINE GOVERNORS 



257 



tion with variation of load. As the governor adjustments are 
brought about only by changes in speed, there is a definite speed 
and definite governor position corresponding to each load. 

Hence the " constant-speed " governor is an anomaly because 
(i) the governor cannot act until there is a change of speed, 
and (2) the governor cannot maintain the configuration of valve 
gear corresponding to different loads unless it runs at different 
speeds for different loads. 

However, with well-designed governors properly adjusted, 
the amount of variation is small and isochronism is approached 
sufficiently close for practical purposes. 

If Wi, W2 and n are respectively the lowest, highest and mean 
r.p.m. of the engine, then the degree of regulation or coefficient 
-fii 



of regulation is e 



'■, which would of course be zero with 



isochronous governing.* 

(b) The four essentials of a good governor are (i) " closeness " 
of regulation, i.e., small coefficient of regulation, (2) quickness of 
regulation, (3) stability or posi- 
tiveness, and (4) power to move 
the parts controlled and to re- 
sist disturbing forces. 

(c) Engine governors may be 
divided into two classes, — the 
" Pendulum " or " Fly-ball " 
Governor, and the "Shaft" 
Governor. 

137. Pendulum Governors, 

(a) The simple pendulum, coni- 
cal, fly-hall or Watt governor is 
shown in Fig. 114. Correspond- 
ing to each different speed at 
which the vertical spindle and weights revolve, there is a definite 
height of cone Qi) at which the centrifugal force (C) and weight 

* It is common practice to speak of the "percentage of speed variation," — 
thus an engine speed may be said not to vary in excess of 2\ per cent. Such a 
statement is ambiguous, — ■ by some it is used to refer to the degree of regulation 
as defined above and by others to refer to the percentage of variation above, or 
below, the mean speed (i.e., to approximately one-half the degree). Hence the 
meaning of the term should always be defined if used at all. 




Watt Governor. 



258 



HEAT-POWER ENGINEERING 



of ball (W) will give a resultant (R) which will be in line with 
the link j-2, which is the condition for equilibrium. For such 
conditions the moments of C and of W about j must evidently 
be equal ; thus, 

Wr = Ch (269) 

But C = —oi^~ = ■ , (270) 

g 12 35,200' 

in which co is the angular velocity in radians per second, r is the 
radius in inches, and n is the r.p.m. Substituting this value of 
C in Eq. (269) and solving gives for the height of cone 



35.200 

71^ 



(271) 



Therefore the height of cone has the same definite value for 
each rotative speed regardless of the length of arm, the method 
of suspension, and the weight of the ball. Thus in Fig. 115 the 




heights of cones (to intersection of arms, produced if necessary) 
are all equal when all weights revolve at the same speed. 

(b) The motion necessary to change the steam supply is 
obtained from the collar of the governor. By referring to Fig. 

114, it will be evident that 
for a given change of speed 
7 the collar lift ij) is twice 
I the change in height of 
■^ cone A^, when upper and 
§ lower arms are equal in 
3 length, that is, when the 
I governor is rhomboidal in 
form. 

Fig. 116 gives the 

heights of cone for speeds 

between 60 and 120 r.p.m., 

r.p.m. It also shows the 

AA2, etc.), corresponding to 




Fig. 116. 

advancing by increments of 10 
different changes in height (AAi, 



STEAM-ENGINE GOVERNORS 



259 



this increment. It is evident that a given amount of collar 
movement may be obtained with less variation in speed, i.e., 
with closer " regulation," when the r.p.m. is low than when high; 
therefore, these governors are 
usually operated at rather low A\ 
speeds. This results in their ca\J/& 
having little " power " to re- T 
sist disturbances which tend to {h) 
move the collar, and to over- 
come resistance offered at that 
point. Such governors are 
therefore ordinarily used only 
when the parts to be moved by 
the collar are light of weight 
and practically frictionless. 

(c) The Weighted Conical or 
Porter Governor is shown in 
Fig. 117 and differs from the 
Watt governor in the addition 
of the central weight Q which 
rests on the collar, and for a 
given speed causes the weights 
to revolve in a lower plane (i.e., 
with height of cone greater) 
than in the simple form. Evi- 
dently, within limits, a given height of cone can be had at any 
speed by merely placing the right amount of weight at Q. 

At the collar, in the figure, is drawn the triangle giving the 

component 5 of — along the link 1-2. The ball is subjected to 

forces S, C, W, and a resultant tension L (in link 3-2) which must 

point toward the pivot 3. These forces are shown at (a) in the 

figure, from which it is evident that the vertical component of 

• Q O Q r 

5 is — and the horizontal component H is — tan 6 = —-r , since 

Y 

r = tan 6. For equilibrium the moments about 3 of the horizon- 
tal and vertical forces or components must be equal, and therefore 
(remembering that L passes through 3), 




Fig. 117. — Weighted Governor. 



c 



26o HEAT-POWER ENGINEERING 

Substituting the second value of C from Eq. (270) and solving 
for the height of cone gives* 

"-hi^y^- (^7.) 

Comparison of this equation with Eq. (271) will show that it 
is possible for the loaded governor to have the same height of 
cone, and same degree of regulation for a given collar move- 
ment, with high speeds, that can be obtained with the simple 
conical governor with low speeds only. The " loaded " governor 
is much the more powerful of the two because of this fact. 

(d) Eqs. (271) and (272) show that to have 
isochronous governing {n = constant) the 
height of cone (h) must be constant. Thus 
in Fig. 118 the path of the ball must be such 
that the sub-normal to the curve is constant. 
As this is the property of the parabola, the 
ball should be guided over such a path for this 
kind of governing. In such case, at the given 
speed, the ball would be in equilibrium at any 
and all points on the guide ; that is, the forces 
'^' ^^ ■ would always be in equilibrium. 

Such an arrangement is, however, of no commercial value 
because (i) if a disturbance increased the speed slightly the 
equilibrium would be destroyed, the centrifugal force would pre- 
dominate, and the ball would seek the extreme position against 
the outer " stop " b; (2) a decrease of speed would cause the 
weight to move to the inner stop a; and (3) there is no definite 
place for the ball at the speed of isochronism — it is balanced at 
any position on the guide; whereas to be of practical value there 
must be a definite position of ball corresponding to each differ- 
ent load to which the engine is subjected. Hence, while this 
governor is ideal as regards constancy of speed, it is unstable 
and of no commercial value. It serves as a limit which actual 
governors may be made to approach as closely as is possible 
without introducing instability. 

(e) Fig. 119 shows an arrangement in which the path of the 
ball is a circular arc approximating the parabolic path, but de- 

* Note that this equation applies only when the governor linkage is rhomboidal 
in arrangement. If the arrangement is like that at {b) in Fig. 117 the formula must 
be modified. 




STEAM-ENGINE GOVERNORS 



261 



parting therefrom somewhat in order to have the difference 
between h^ and hi sufi&cient to insure stability. Such an arrange- 
ment is described as a governor with crossed arms. 

With the governor previously described, which has the suspen- 
sion point located on the spindle, the path of the ball departs 





Fig. 119. 

widely from the parabola, hence such governors do not give close 
regulation except when the collar movement is small. 

(f) Isochronism can be approached by having the point of 
attachment between links offset from the weight arm, as at a in 
Fig. 120, or using the equivalent hent arm, as at h. The theory 
of this type of governor will not be included here.* 

Fig. 121 shows another arrangement of governor with which 
isochronism can be approached.* 

(g) Eqs. (271) and (272) apply only in the ideal case in which 
there is no resistance to be overcome. If the collar and pins have 
friction, the speed of the governor must change a considerable 
amount, Aw, before the centrifugal force is changed by a suffi- 
cient amount to enable it to overcome this resistance and cause 
the collar to start to move. Thus, if the change in speed neces- 
sary to overcome the resistance when the weights tend to move 
out equals that when the tendency is inward, there can be a 
change in speed equal to 2 A» without movement of the collar. 
Evidently the degree of total regulation is similarly affected. 
The greater the collar friction the larger the influence, hence the 
collar friction, the resistance of all parts moved by the collar, 
and the friction of the governor parts must be as small as possi- 
ble, if close regulation is desired. 

* See Tolle, "Die Regelung der Kraftmaschinen," Julius Springer, publisher, 
Berlin. 



262 



HEAT-POWER ENGINEERING 




138. Spring-balanced Fly-ball Governor. In the fly-ball gov- 
ernors so far discussed the moments of the centrifugal forces 

acting on the balls were balanced by the 
moments of the gravity forces. Some gov- 
ernors are so arranged that the centrifugal 
forces (or their moments) are practically 
entirely balanced by one or more springs, 
as in Fig. 122. In other governors the cen- 
trifugal force is balanced by a combination 
of gravity and springs. 

The degree of regulation of the governor 
shown in Fig. 122 can be adjusted by means 
of the nuts N, which can be used to change the initial compression 
of the spring. This governor operates on the same principle as 
the simple centrifugal "shaft" governor described in the next 
section. There are many different arrangements of governors of 
this type. They may be made to operate at high speed and have 
considerable power, and they can be adjusted to give " close" 
regulation. 

139. Elementary Shaft Governors, (a) The shaft governor 
is so called because it is mounted either in the flywheel or in 
a governor case carried by the main shaft of the engine. 

(b) The elements of the simplest form of this governor are 
shown in Figs. 123 to 125. Referring to Eq. (270), it is seen that 




iW\/WV-"/M. 



/"A W 

5->j // 



Fig. 123. Fig. 124. 

if the speed of rotation is constant the centrifugal force C with a 
given weight varies directly with the radius r. Thus in Fig. 123, 
with constant speed = Wi, the ordinates (C) of the line Oni show 
the manner in which the centrifugal force increases as the weight 



STEAM-ENGINE GOVERNORS 263 

W is moved outward from the center of the shaft. 0^2 shows 
the same thing for a higher constant speed n^, and similar hnes 
could be drawn for each other speed. 

(c) In Fig. 124, 5 is a spring with end at when free. The 
ordinates (F) of curve Of show the increase of the spring force 
with the elongation 8. As the curve is similar in character to 
those in Fig. 123, it would be possible to place the spring in the 
flywheel, with end at the center of rotation, and thus cause 
Of to coincide with one of the On- 
curves. The centrifugal force would 
then be balanced by the spring pull 
in all positions of the weight, for 
that particular speed. Hence this 
arrangement would give isochro- 
nism. The speed at which this 
equilibrium occurs depends of course 
on the strength of the spring. 

(d) If a in Fig. 125 is the position 
of the center of the ball when against 
the inner stop, then when the weight 
is in the "inner position" the spring will have elongation equal 
to Oa. The extension of the spring with the weight in the inner 
position is called the " initial elongation." In adjusting the spring 
to give isochronous governing, the initial elongation 61 must be 
equal to the distance Oa, which is equal to ri. 

(e) The isochronous shaft governor is an unstable one; any 
change from the speed of isochronism causes the weight to move 
to one or the other extreme position ; and at the speed of isochro- 
nism the weight is in equilibrium at any position in its path, 
that is, has no definite position. Therefore, this governor is of 
no commercial value, but is the limit which actual governors may 
be made to approach as closely as is possible without introducing 
instability of action. 

(f) In order to have stable governing, there must be definite 
positions of the weight W for each different load on the engine. 
If the end of the spring, when not under tension, is at 0', to the 
right of the wheel center in Fig. 126, instead of at 0, then the 
line of will cross the o«-curves; point i will correspond to a speed 
equal to n^, point x' to Ux, and point 2 to n^; thus, when the weight 
is at a the spring pull will be balanced by the centrifugal force 




264 



HEAT-POWER ENGINEERING 



when the speed is Ui, at x there will be equilibrium if the speed 
is fix, and at b the forces are equal when the speed is W2. 

With such an arrangement there is a definite position of the 
weight at each different speed, thus the arrangement is stable. 





Fig. 126. 

If the position of W fixes the power developed by the engine, 
then there will be a different speed for each different power 
output. 

The line 1-2 is sometimes called the Characteristic Curve 
(C-curve), as its position with respect to the constant speed 
curves, On, indicates the character of the governing. 

(g) If a is to be the inner position of the weight, and fii the 
lowest speed, then point i is fixed. The speed corresponding to 
position b is determined by the slope of the Characteristic Curve 
1-2 relative to the constant-speed curves, and is dependent on 
the distance 00' or on the distance 5i. If o' coincides with 0, 
the initial elongation 81 = r^, and the governor would be isochro- 
nous, as the C-curve would coincide with otii. The greater the 
distance 00' is, i.e., the smaller the initial elongation 81 (compared 
with fi) the greater will be the speed variation between limits 
a and b, and the greater will be the stability, and vice versa. 

(h) The adjustment of a governor is divided into two parts 
as follows: — (i) The initial elongation of the governor spring, 
would be increased (by means of nut at N in figure) until the best 
degree of regulation that is consistent with stability is obtained. 
Note that the degree of regulation is dependent only on the 
amount of the initial elongation, and that it is independent of 
the strength of spring and of the weight of ball. 



STEAM-ENGINE GOVERNORS 



265 



(2) After the spring has been adjusted to give the proper 
degree of regulation, the speed can be changed to any desired 
value, within reason, by changing the weight W. If the weight 
is reduced the speed will increase until the centrifugal force 
balances the spring pull; if increased, the effect on the speed will 
be the opposite. 

(i) In Fig. 127 the weight W is mounted on an arm pivoted 
at J and with spring 5 attached at 1. If it is considered that 
the arc ah here approximates path 
ab in Fig. 126, the spring 5 would 
have initial elongation 5i, the same 
as in that case. Evidently spring 
vS can be replaced by spring S' if 
the latter is made l/V times as 
strong {W remaining the same) 
and if the initial elongation is 
made equal to {V /l)h- 

This arrangement contains the 
elements of the more common 
forms of commercial shaft gov- 
ernors. It is adjusted in the same 
manner that was described in (h) for the simple case. 




Fig. 127. 



140. Commercial Types of Shaft Governors, (a) In general, 
the commercial shaft governor has one, or two, pivoted " weight 
arms," the centrifugal force acting on which is balanced by one 
or more springs which are so adjusted that there is a differ- 
ent speed and a corresponding definite and distinct position 
of the arm, or arms, for each different load on the engine. 
The " weight arms " are connected either directly, or by 
links, to the eccentric, so that for each speed there is a 
definite and distinct position of the eccentric, a corresponding 
cut-off, and a definite amount of power developed. If the load 
changes, the speed of the engine will also change until a cut-off 
is found which gives the right amount of power to meet the 
demand. 

If the governor is of good design and properly adjusted, the 
total amount of speed variation is very small (being from i to 2^ 
per cent of the "normal " or average speed); thus the speed is 
practically constant. 



266 



HEAT-POWER ENGINEERING 



There are two general types of shaft governors, — the "Centrif- 
ugal" and the "Inertia." 

(b) The Sweet governor, which was one of the earliest of the 
centrifugal governors and which is still widely used, is shown in 
Fig. 128. Pivoted to one of the arms of the flywheel, or governor 
wheel, is a "weight arm," which has a heavy head W. When 
the engine is not running, this weight arm is held in the "inner" 
position (that shown in full lines) by the leaf spring S. After 
steam is turned on, the arm will remain in this position until the 
speed has reached a certain point (for example, say 198 r.p.m.), 




Fig. 128. — Sweet Type of Centrifugal Governor. 



when the centrifugal force C will just balance the spring pull. 
If the speed is raised further, the increased centrifugal force will 
cause the arm to move outward until, at some speed (say 202 
r.p.m.), it reaches the extreme "outer" position (that shown by 
the dotted lines). At the "normal" speed (200 r.p.m.) the 
weight arm would be about midway between these extreme 
positions; and for every other speed (between the 198 and 202 
r.p.m.) there are definite positions of the arm. 

In the example the total variation in speed is 2 per cent of the 
normal r.p.m. By changing the adjustment of the spring, how- 
ever, the amount of variation can be altered, but if it is made too 



STEAM-ENGINE GOVERNORS 



267 



small the friction and inertia of the valve gear, and the other 
disturbances, will make the action of the governor uncertain, — 
so there is a practical limit to the closeness of regulation. 

Again referring to Fig. 128, it is seen that the arm carrying the 
eccentric is pivoted at P to one of the arms of the wheel, and is 
connected by a link L to an extension of the weight arm. When 
this latter is in the inner position, or is "in," the center of the 
eccentric is at E, the position for the latest cut-off; and when it is 
"out," the eccentric center is at e, the position for zero cut-off. 

The manner in which the governor operates is as follows: 
When the engine is standing still, the governor holds the eccen- 
tric in the position E for the latest cut-off. When steam is 
turned on, the engine will speed up until a certain r.p.m. is 
reached, at which the governor arm will begin to move out, thus 
shifting the eccentric towards e and decreasing the cut-off. This 
movement will continue until a position is reached at which the 
power developed just equals the load, and as long as this latter 
remains constant the governor arm will remain in this position. 
Now, if the load is reduced, the engine will speed up (tending to 
run away), and this causes the weight arm to fly out, shifting the 
eccentric nearer to e and reducing 
the power developed until it be- 
comes again equal to the demand. 
Similarly, if the load is increased, 
the speed of the engine will de- 
crease, and, as the weight arm 
moves "in," the cut-off will be 
increased, until at some position 
of the arm a balance is again 
reached between the power and 
the load. 

Fig. 129 shows another "centrif- 
ugal" shaft governor; but in this 
case there are two weight arms, symmetrically placed, instead 
of one. In its action, this governor is identical with that which 
has just been described. 

(c) Fig. 130 shows the Rites Inertia Governor, which consists 
of a long weight arm (WW), an eccentric pin E, and a spring. 
The arm is pivoted at P, close to the shaft, and its end W is 
heavier than W, so the center of gravity is at G. The position of 




Fig. 129. — Centrifugal Governor. 



268 



HEAT-POWER ENGINEERING 



the parts shown in full lines is for latest cut-off, and is the one 
occupied when the engine is not running; that shown by the 
broken lines is for the earliest cut-off. In the former position, 
the arm is said to be " in," and in the latter, " out." The direc- 
tion of rotation is shown by the arrow. The governor will not 
operate satisfactorily if the direction of rotation is reversed with- 
out making changes in the governor itself. 

As the engine starts up, the governor arm remains in the inner 
position until a certain speed is reached, when the centrifugal 




Inertia Governor. 



force C, acting on the weight arm, becomes sufhciently great to 
balance the spring pull. Then, with a further increase in speed, 
the weight arm will move out (the eccentric meanwhile moving 
toward e) until a sufficiently early cut-ofif is obtained. 

Now, if the load falls off the engine will speed up, and the 
increased centrifugal force will cause the weight arm to move 
out until the cut-off is reduced to the proper amount, the action 
being just the same as in the case of the centrifugal governor. 
However, in addition to the centrifugal force acting on the arm, 
there is also an inertia force which assists the movement. 

The inertia of the weight arm acts in this manner: As the 
engine speeds up the governor arm tends to continue to rotate 



STEAM-ENGINE GOVERNORS 



269 



at its old speed, because of its inertia, and hence lags behind the 
wheel, moving with respect to the latter in the direction shown 
by the arrows / and / in the figure. It is seen that this movement 
is in the same direction as that caused by the centrifugal force C. 
Again, if the load is suddenly increased the engine will slow down, 
but, because of its inertia, the weight arm will continue at its 
old speed, thus gaining on the flywheel, and again assisting the 
centrifugal force in changing the position of the eccentric and 
weight arm with respect to the crank. 

It is seen that the inertia governor is primarily a centrifugal 
governor, but that, in addition, the weight arm is so pivoted, 
and has its weight so distributed, that its inertia assists in mak- 
ing the adjustment, and that the more sudden the change in the 
load the greater will be the assistance it renders. 

In this form of governor the eccentric, or eccentric pin, is 
usually mounted directly on the weight arm. Sometimes the 
eccentric is keyed directly to the fulcrum pin on the end opposite 
that to which the arm is fastened. With these arrangements, 
in order to have the inertia of the weight arm act in the right 
direction, the fulcrum pin must he placed on the side of the shaft 
opposite to the crank pin, when an "external" valve is used, and 
on the same side when the valve is " internal " (Section 143). 

On "center-crank" engines the governor is frequently placed 
in the outer side of the 
wheel, in which case, since 
the shaft does not extend 
beyond the governor wheel, 
the arrangement can be 
that shown in Fig. 130. If, 
however, the governor is 
placed on the side of the 
wheel next to the engine 
frame, both the governor 
arm and the eccentric must 
be made to surround the 
shaft in the manner shown 
at a, Fig. 130. 

Fig. 131 shows the Arm- 
strong governor, which is of the inertia type. The weight W is 
mounted on the end of the leaf spring S, and is subjected to cen- 




Fig. 131. — Armstrong Governor. 



270 HEAT-POWER ENGINEERING 

trifugal force C, and also to inertia force / or /' when sudden 

change occurs. 

(d) For both forms of shaft governors it has been seen : 

(i) That there is a definite speed, cut-off, and power for each 

position of the weight arm. 

(2) That when the arm is "in," the speed is the lowest and 
the cut-off is the latest; whereas, if the weight arm is "out," the 
reverse is the case. 

(3) That an increase in load decreases the speed and causes 
the arm to move "in," which gives a later cut-off; whereas, the 
.effect of a decrease in load is the reverse. 

(4) That, for close regulation, the friction and inertia of the 
valve-gear parts must be small, and especially is this necessary 
when the inertia form of governor is used. 

(5) The adjustments of spring to obtain the desired degree of 
regulation, and of weight to obtain the speed wanted, are made 
in the manner outlined in Section 139 (h) for the elementary 
governor. 

There are almost an unlimited number of forms of shaft 
governors, but all of them are merely modifications of those 
which have been described. 



CHAPTER XIX. 

THE VALVE GEARS OF STEAM ENGINES. 

141. Introduction. It is assumed that the reader is already 
famiUar with the arrangement and operation of the simple steam 
engine having the plain slide valve, and that he is able to use 
at least one kind of " valve-gear diagram "for the analysis or 
design of a simple " D-valve." The purpose of this chapter is 
mainly to review certain definitions, to bring out certain con- 
ceptions which will be useful in the later discussions, and to give 
a brief discussion of the different types of valve gears used on 
steam engines. 

142. The Engine. Definitions, (a) The crank end (C. E.), or 
front end, of the cylinder, or valve, is the one nearest the crank. 



MODEL OF 
SINGLE ACTING 

ENGINE cranVEnd 




Steam Chest 



or next to the engine frame. The opposite end is the head end 
(H. E.), or back end. 

(b) The forward (Fd.) stroke of the piston or valve is that 
towards the crank. The return stroke is the hack (Bk.) stroke. 

271 



272 HEAT-POWER ENGINEERING 

(c) Fig. 132 shows a model of a simple single-acting engine 
with piston and valve driven by crank and eccentric pins opera- 
ting in Scotch yokes, or slotted crossheads. It is evident that 
with this arrangement the valve and piston will have simple 
harmonic motions, and in consequence the analysis of the valve 
action is a simple matter. 

The motions, with this arrangement, are exactly the same as 
would occur if the engine had connecting and eccentric rods of 
infinite length. 

(d) Steam engines, of course, have connecting rods and eccen- 
tric rods of finite length, and the " angularity " of these rods 
causes the motions of piston and valve to depart slightly from 
the true harmonic. The eccentric rods are usually so long, how- 
ever, when compared to the radius of the eccentric crank, that 
the departure in the case of the* valve is negligible. If the 
analysis of motions is to be only closely approximate, the motion 
of the piston may also be taken as true harmonic, which simplifies 
the problem. 

(e) The crank is on dead center when the piston is at the end 
of the stroke, and is then horizontal on horizontal engines. 
When the piston is at the head end of the cylinder, the crank is 
on the " head-end dead center "; when at the other end, it is on 
the " crank-end dead center." 

^(f) The eccentric (ecc. or E) is really a crank with pin of such 
large diameter as to surround the shaft. In the following dis- 
cussion the term " eccentric " will be used as applying to the 
center of this pin. Like other cranks, the eccentric has dead- 
center positions. 

(g) The throw of the eccentric is the " eccentricity " or length 
of the crank. (There is a lack of agreement in the use of the 
term "throw," some using it in the sense given and others as 
meaning the total movement of the valve or " travel.") 

143. The Valve. Definitions, (a) Fig. 133 shows the longi- 
tudinal section of a simple D-valve suitable for a single-acting 
engine which takes steam at only the head end of the cylinder. 
This valve is arranged to admit steam to the cylinder past the 
left outer edge (when steam edge s of the valve passes to the 
right of the steam edge S of the port) , and to exhaust the steam 
from the cylinder past the left inner edge (when the exhaust 



THE VALVE GEARS OF STEAM ENGINES 



73 



edge u of the valve moves to the left of the exhaust edge U of 
the port). 

(b) The width of the port is the distance SU m the figure. 

(c) The valve shown is 
called an external valve. If 
the valve admitted steam to 
the cylinder past its inner 
edge and exhausted at the 
end, it would be an internal 
valve, and would have to be 
of different design from that 
shown here. Unless other- 
wise stated, the valve will be 
assumed to be external. 

(d) The terms " steam chest,'' 




Fig. 133- 

and '' valve seat 



^exhaust cavity,' 
should not need explanation (see Fig. 133). 

(e) The valve is central (or in mid-travel), with index at in 
Figs. 132 and 133, when the eccentric is vertical, either up or 
down. 

(f) The lap of the valve is the distance between the valve edge 
and the port edge with which it operates, when the valve is 
central. The outside lap (or outer lap) is that of the outer edge, 
and the inside lap is the lap of the inner edge of the valve. The 
steam lap (S. L.), see Fig. 133, and the exhaust lap (Ex. L.) are 
respectively those of the steam and exhaust edges of the valve. 
The lap is positive if the port is closed when the valve is cen- 
tral and negative if open. (Negative lap is sometimes called 
" clearance.") 

(g) The valve opening is variable and is dependent on the dis- 
placement of the valve; but the term is usually understood as 
referring to the maximum width of the opening unless otherwise 
stated. 

(h) The travel of the valve is the stroke or total amplitude of 
its motion. If the valve is direct-driven, the travel is equal to 
the diameter of the eccentric circle. 

(i) The term "displacement," when applied to the valve, will be 
understood to mean the distance the center of that part has been 
moved from its central position; and in the case of the eccentric 
on a horizontal engine it will be the horizontal distance from the 
center to the vertical center line of the shaft. 



2 74 HEAT-POWER ENGINEERING 

(j) The four periods of operation of the valve are admission, 
expansion, exhaust, and compression. 

(k) The four principal valve events are admission (A), cut-off 
(C), release (R), and compression (K). The fotu minor events 
are maximum displacement of the valve to the right (M), same 
to the left (m), valve central and moving to the left (Q), and 
central but moving to the right (q). 

The letters given in the parentheses in the above list will be 
used to indicate the respective events on the diagrams which are 
to follow. 

(1) Unless it is specifically stated to the contrary, it will always 
be assumed in the following discussion that the engine is horizontal, 
with cylinder to the left of the crank shaft, that an " external valve " 
is used, and that the crank rotates in a clockwise direction. 

144. Action of the D-Valve and Eccentric, (a) When the 
valve is driven by a Scotch yoke, it is seen, by referring to Fig. 
132, that (i) the valve is central when the eccentric is on the 
vertical center line OY through the center of the shaft, (2) 
the valve will be in this position whether the eccentric OE is 
vertical upward or downward, and (3) that at all times the dis- 
placement X of the eccentric E equals the displacement x of the 
valve. 

(b) In Fig. 133 it is seen that the valve must be displaced to 
the right a distance equal to the steam lap before opening to 
steam occurs, and that any further displace- 
ment represents opening. In Fig. 134, in 
which the radius of the circle equals the eccen- 
tric throw, the distance from the eccentric 
center (anywhere on this circle) to the axis 
qQ is the valve displacement. On this figure 
the " steam-lap line ''AC has been drawn at 
a distance equal to the steam lap to the right 
of gQ. Hence the steam edge is open an 
amount equal to the horizontal distance the eccentric is to the 
right of line AC. In Fig. 133 it is seen that the valve must 
be displaced to the left a distance equal to the exhaust lap 
before exhaust opening occurs, and that further displacement 
in that direction represents the amount of opening. In Fig. 
134 the exhaust-lap line KR is at a distance which equals the 




THE VALVE GEARS OF STEAM ENGINES 275 

exhaust lap to the left of Qq. Hence the exhaust edge of the 
valve is open an amount equal to the horizontal distance that the 
eccentric is from KR, if it is to the left of that line. If the ex- 
haust lap is negative, KR will be to the right of qQ. 

(c) Starting with the eccentric center at q in Fig. 134, the valve 
is evidently central and moving to the right, since the rotation is 
clockwise. When the eccentric reaches A, the valve displace- 
ment equals the steam lap, and admission occurs; when at B, the 
valve is displaced a distance BO to the right and its steam edge 
is open an amount equal to BD; at M the valve has maximum 
displacement and maximum steam opening; at C the valve, 
now moving to the left, has displacement equal to the steam lap, 
and cut-off is occurring ; at Q the valve is central and its edges are 
overlapping by amounts equal to the respective laps; at R the 
valve is displaced to the left an amount equal to the exhaust lap, 
and is opening to release; at m the valve displacement is maximum 
to the left, and maximum exhaust opening is reached; and at K 
the displacement is equal to the exhaust lap, so that exhaust 
closure or compression is beginning. The amounts of openings 
to steam and exhaust are shown by the lengths of the horizontal 
section lines. Fig. 134 may be called a rectilinear diagram of 
valve displacements. 

(d) Note that admission and cut-ofif are controlled by the 
same valve edge (steam edge) but with valve motions opposite. 
This is apparent not only from Fig. 133, but can be seen from 
line ^C in Fig. 134. Similarly, compression and release are 
controlled by the same edge (exhaust 
edge). Valve events controlled by the 
same edge may be called conjugate 
events, and it is important to note 
that changing the lap affects in opposite 
manner the two conjugate events which 
the edge controls. 

(e) Fig. 135 shows a polar diagram 
of valve displacements, corresponding 
to the different eccentric positions. 
This diagram is not necessary here, but 
it will be of use in connection with a valve diagram which will 
be discussed later. Given any eccentric position OE, the valve 
displacement x = OB' is laid off as OB along OE. The locus 




276 



HEAT-POWER ENGINEERING 



of point B is OAMCORmK, which is composed of two circles. 
The locus for displacements to the right is shown by the heavy 
line, and that for displacements to the left by the light line. 
Given any eccentric position such as OE, the intercept OB is 
the valve displacement (here to the right). 

Arc AC is the steam-lap line, and is struck with the steam 
lap as radius. Arc RK is the exhaust-lap line, with radius 
equal to the exhaust lap. 

When the eccentric is at Og^, the valve is central; when it ex- 
tends through OA , the valve displacement equals the steam lap, 
and admission occurs ; when at OM, the displacement and steam 
opening are maximum; when through OC, cut-off occurs; at OQ, 
the valve is central; when through OR, release takes place; at Om, 
the displacement and exhaust opening are maximum; and at OK, 
compression begins. The lengths of the radial section lines show 
the amounts of opening of the steam and exhaust edges. • 




> Positive 6 

ExhanstLajp 



Fig. 136. 



(f) Fig. 136 shows a double-end D-valve 
such as is used on double-acting engines. 
The crank-end displacement diagram will 
be similar to the head-end diagram ro- 
tated through 180 degrees. 

145. Relative Valve and Piston Posi- 
tions, (a) Consider the piston driven by 
a Scotch yoke, as in Fig. 132. When the 
crank is on head-end dead center, as in 
Fig. 137, the valve should have opened a 
slight amount, called the lead, principally 
in order to furnish steam to fill the clearance space and replace the 
vapor lost by initial condensation before the stroke starts. Hence 




THE VALVE GEARS OF STEAM ENGINES 



277 



the eccentric at this time must be at OB, with displacement equal 
to lap plus lead. The angle a = gOB is called the angle of 
advance, and it is seen that, for the valve to have lead and the 




Fig. ij 



proper direction of motion when the crank is on dead center, the 
eccentric must precede the crank hy an angle equal to 90 degrees plus 
angle of advance. Thus if rotation 
were counter-clockwise the eccentric 
would be at OB' when crank is 
at OP. 

(b) Fig. 138 shows the successive 
critical crank positions during one 
complete revolution of the crank. 
These crank positions are located 
90° + a behind the corresponding 
eccentric positions. The figure also » 
shows the development of the indi- | 
cator diagram during the revolution. |, 

5 

146. Elliptical Diagram. To show I 
at a glance the simultaneous dis- 
placements of the valve and piston 
throughout the complete revolution 

of the engine, the displacements of ^ig. 139- - Elliptical Diagram, 
the valve may be plotted as ordinates on the corresponding 
positions of the piston as abscissas. These coordinates can be 




278 



HEAT-POWER ENGINEERING 



obtained directly from the corresponding crank-pin and eccentric 
positions, as shown in Fig. 139 (a), or may be obtained from other 
valve diagrams which will be discussed later. The resulting 
figure is an ellipse, as shown in Fig. 139 (b), in which valve dis- 
placements to the right are positive ordinates and those to the 
left negative. 

Lines AC and RK are the head-end steam and exhaust lines 
and are drawn at distances from qQ equal to these respective 
laps. (If the exhaust lap is negative, RK will be above qQ.) 
The valve events are lettered in accordance with the notation 
adopted in Section 143 (k). The valve openings are shown by 
the lengths of the section lines. The opening at the beginning 
of the stroke is the lead. 

If an indicator diagram for the head end were drawn just 
below Fig. 139, the piston positions for the valve events could be 
found by vertical projection. 

As both ends of the valve have the same displacement, the 
same ellipse would be used for the crank end, but the steam lap 
would be located below and the exhaust lap above qQ (if positive) . 

The elliptical diagram shows at a glance the complete action 
of the valve, and shows how the valve opening varies with the 
piston positions. The part of the diagram above the steam-lap 
line may be considered as a Diagram of Steam Openings. Simi- 
larly, that part lying below RK is a Diagram of Exhaust Open- 
ings. 




(a) * ■ ib) 

Fig. 140. — Sweet Diagram. 

147. The Sweet Diagram. In Fig. 140 (a) is shown a diagram 
of valve and eccentric displacements similar to Fig. 134, and 



THE VALVE GEARS OF STEAM ENGINES 279 

Fig. 140 (b) shows the diagram rotated backward (counter- 
clockwise) through an angle of 90° + a, which is the angle at 
which the crank follows the eccentric. When the crank is at any 
location OP in Fig. 140 (a) and eccentric at corresponding posi- 
tion OB, the valve displacement is oB and its opening is DB. 
In Fig. 140 (b), with crank in same position OP, the distance oB, 
measured perpendicularly to qQ, gives the valve displacement, 
and DB is the valve opening. Thus the valve displacement and 
opening for any crank position can be obtained directly from 
Fig. 140 (b), which is called the " Sweet Diagram," and there is 
no necessity of finding the corresponding eccentric position. 
■ In constructing the Sweet diagram a circle is drawn with 
radius equal to the eccentric throw; the axis qQ is at angle a 
with OX ; and lap lines A C and RK are drawn at distances from 
qQ equal to the laps. OP a is the crank position for admission; 
OM, for maximum displacement; OPc, for cut-off; OQ, for valve 
central; OPr, for release; OPr, for compression. The openings 
are shown by the lengths of the section lines, and when the crank 
is on head dead center the opening is the lead. The foregoing is 
for the head end of a valve having positive exhaust lap. If the 
exhaust lap is negative RK would be above qQ. For the crank 
end of the valve the steam lap would be located below qQ, and 
the exhaust lap, if positive, above that Hne. The little " Pilot 
Diagrams " show the relation of crank and eccentric for all valve 
events. 

The elliptical diagram can be obtained from Fig. 140 (b) by 
using distances oB as ordinates on the horizontal projection of 
the crank pin P. 

148. Zeuner Diagram. In Fig. 141 (a) is shown a polar dia- 
gram of valve and eccentric displacements similar to Fig. 135, 
and Fig. 141 (b) shows the same diagram rotated backward 
through the angle 90° + a. In Fig. 141 (a), when the crank is 
at OP and eccentric at OE, the valve displacement is OB and 
its opening is DB. In the Zeuner diagram, Fig. 141 (b), with 
crank in the same position OP, OB is the displacement and DB 
is the opening. The crank positions for all events (major and 
minor) are shown and lettered on the figure, and the lengths of 
the radial section lines show the valve openings for the different 
crank positions. The lead is the opening when the crank is on 



28o 



HEAT-POWER ENGINEERING 



dead center. The Zeuner diagram for the crank end is similar 
to that for the head end rotated through i8o degrees. In Fig. 




Fig. 141. — Zeuner Diagram. 

141 (b) the " Pilot Diagrams " show the relative positions of 
crank and eccentric at all valve events. 

The elliptical diagram can be easily obtained from the 
Zeuner diagram. 

149. Bilgram Diagram, (a) The foregoing diagrams are useful 

for analyzing the action of a valve when its dimensions and those 

of the eccentric are known. They are difificult to use, however, 

in designing a new valve gear, that is, in determining the valve 

laps and the eccentric throw and 

^ angle of advance, which will give a 

Q Fixe^ proposed steam distribution in the 

,-? Pom^ cylinder, with specified widths of 

Pi. J"! ^-—-^L ^" I-4-X openings. The Bilgram diagram 

■^ has the advantage that it can be 

readily used either for analysis or 
for design. 

(b) Fig. 142 shows the principle of the Bilgram diagram. 
On it the line OQ is made equal to the eccentric throw and is at 
angle a (the angle of advance) with OX. Q is a fixed point on 
this diagram and is called the Lap-Circle Center. The Funda- 
mental Principle on which the construction and use of the Bil- 
gram diagram is based may be stated thus : The length of the per- 
pendicular (QD in Fig. 1^2) from the lap-circle center {Q) to the crank 
{OP), produced if necessary, is the valve displacement corresponding 




Fig. 142. — Bilgram Diagram. 



THE VALVE GEARS OF STEAM ENGINES 28 1 

to that crank position. Proof. — When the crank is on dead 
center (at OP' in Fig. 142) the eccentric is at OE and angle 
EOY = a. Now if the crank rotates through angle jS to OP, 
the eccentric moves through the same angle to B, and the valve 
then has displacement equal to D'B. Now angle QOX = a 
and XOD = ^. Then if QD is drawn perpendicular to OP 
(produced), it is evident that triangles OQD and OBD' are equal 
and that QD = D'B; hence the perpendicular QD gives the valve 
displacement when crank is at OP, which proves the " funda- 
mental principle." 

The term " perpendicular " used in connection with the Bil- 
gram diagram will hereafter be understood to refer to the length 
of perpendicular dropped from Q to the crank, produced if 
necessary. 

The elliptical diagram can of course be constructed by using 
these perpendiculars as ordinates on piston positions as abscissas. 

(c) Evidently the feet of the perpendiculars will be on a circle 
with OQ as diameter, as in Fig. 143. By subtracting the lap 
from the displacement perpendiculars, the openings of the valve 
are obtained. 

In Fig. 143, with Q as center and radius equal to the steam 
lap, the steam-lap circle BF is drawn; hence the lengths of 




Fig. 143. 

the section lines (drawn radially from Q) in this figure give the 
steam openings for the head end of the valve. Then OA (whose 
extension is tangent to the lap circle) is the crank position for 
admission, as the valve displacement (as shown by the length of 
perpendicular) just equals the steam lap. At OP the opening 



282 



HEAT-POWER ENGINEERING 




is FD and displacement is QD ; at OM the opening is maximum and 
equal to OB ; at OC the opening is zero and cut-off occurs. When 
the crank is on head-end dead center the opening L is the lead. 

(d) Fig. 144 shows the completed Bilgram diagram for the 
head end of the valve. Compared with Fig. 143, it is seen that 

the smaller circle about Q, and 
the crank positions for the ex- 
haust events, have been added. 
The small circle is the Exhaust- 
Lap Circle, with radius equal 
to the exhaust lap. If release 
is to occur when the crank is 
in position OR, the exhaust-lap 
circle must be tangent to this 
line, for then the valve displace- 
'^^" ^'^^' ment (as shown by the length 

of the perpendicular) is equal to the exhaust lap. 

When the crank coincided with OQ the valve was central, and, 

since in this case the valve does not open until the crank has 

rotated clockwise past OQ, the valve is closed when central, 

therefore the exhaust lap is positive. 

(e) The portions of the perpendiculars beyond the exhaust- 
lap circle represent exhaust openings. Evidently exhaust closure, 
or compression, takes place when the extension of the crank is 
tangent to the upper side of the lap circle; thus OK is the crank 
position for compression. When the crank coincides with Oq the 
valve is central ; and, since in this case the exhaust lap is posi- 
tive, the exhaust closure must take place before the valve 
reaches central position; hence OK is below Oq in this case, as 
the rotation is clockwise. 

If the exhaust edge has negative lap, the crank position OR 
would be tangent to the upper side of the exhaust-lap circle, 
and the extension of OK would be tangent to the under side. 

(f) The application to design problems when certain definite 
cut-off, lead opening, and maximum valve opening to steam are 
required, is as follows: In Fig. 145, for the H.E. of the valve, 
starting with the X and Y axes, draw the desired crank position 
OC for cut-off; draw a line (L) parallel to OX and above it at a 
distance equal to the specified lead; and with as center and 
radius equal to the desired maximum valve opening strike an 



TEE VALVE GEARS OF STEAM ENGINES 



283 




Fig. 145- 



arc B in the position shown. From what has gone before, it is 
evident that the steam-lap circle must be tangent to these three 
lines. The location of its 
center Q can usually be 
found as quickly and as 
accurately by trial as 
by geometrical construction. 
Having the point Q deter- 
mined and the steam-lap cir- 
cle drawn, the diagram then 
shows the steam lap and the 
throw and angle of advance 
of the eccentric, which must 
be used to obtain the de- 
sired results. 

If OK in Fig. 145 is the 
desired crank position for 
compression, the exhaust-lap circle would be drawn tangent to 
the extension of this line, with center at Q just found, and its 
radius will equal the exhaust lap. Whether the exhaust lap is 
positive or negative can be determined in accordance with (e) 
in the foregoing discussion. 

(g) For the crank end of the valve, the Bilgram diagram would 
be similarly constructed but rotated 180 degrees with respect 

to the diagram for the head 
end. Q and q must of course 
be diametrically opposite 
each other. Fig. 146 shows 
the crank-end Bilgram dia- 
gram separately; it is usu- 
ally, however, drawn super- 
imposed on the diagram of 
the head end. 

150. Distortion Due to 
Angularity of the Connecting 
Rod. In Fig. 147 is the 
middle of the stroke and the distance oO is equal to the 
length of the rod aP. If an infinite rod is used, the displace- 
ment of the piston oa will of course be equal to the displace- 




Fig. 146. 



2«4 



HEAT-POWER ENGINEERING 




Fig. 147. 



ment of the pin P, which is equal to OA . If, however, a finite 
rod is used these displacements will not be equal. For, if the 
end of the rod a is kept stationary and the other end P is 

uncoupled and swung to A\ 
then oa will be equal to OA', 
which is seen to be greater 
than OA. It will be found 
that no matter where the 
crank is. A' will always be 
to the right of ^. It is evi- 
dent that, owing to the 
*' angularity " of the connecting rod, if one of finite length is 
used, the piston is always nearer the crank end of the stroke than 
it would be ideally, except of course when it is at the end of its 
stroke. 

It follows that: The valve events occur later with respect to piston 
positions during the forward stroke and earlier in the return stroke 
than they would with the Scotch yoke, but their mean is the 
same as this latter gives if the laps are equal. 

The distance ^yl' is the " distortion due to the angularity of 
the rod " and is equal to the difference between the length of 
the rod and its horizontal projection. This distortion is greatest 
when the crank is at right angles to the center line of the engine, 
and decreases to zero at the ends of the stroke. The shorter the 
length of the rod when compared to the crank radius, the greater 
is this relative distortion. 

If the diameter of the crank circle XX' represents the stroke 
of the piston, then, having any position, such as ^', the corre- 
sponding position of the crank pin P may of course be found by 
drawing the " connecting-rod arc " A'P; or if P is known at 
the start, A' may be found from it in a similar manner. 

The angularity of the eccentric rod can be neglected in most 
cases, as the rod is usually very long when compared with the 
eccentric throw. 

151. Valve Diagrams Considering " Angularity " of the Con- 
necting Rod. (a) All the valve diagrams discussed show the 
true positions of the crank; therefore if the positions of the pis- 
ton are not being considered, but only those of the crank, the 
angularity of the connecting rod would not affect the diagram. 



THE VALVE GEARS OF STEAM ENGINES 



^85 



If, however, after the crank positions have been found, the true 
positions of the piston are desired, it will then be necessary to 
consider the angularity. Having already determined the crank 
positions, the corresponding true position of the piston would 
be found by drawing the connecting-rod arcs in the manner 
shown in Fig. 148 (a), {b), (c) for the Sweet, Zeuner, and Bilgram 
diagrams. Should the piston positions be known at the outset, 
then by drawing similar arcs the true crank positions can be 
found, and these would be used in constructing the rest of the 
diagram. 

In the elliptical diagram. Fig. 148 (d), it is evident that the 
angularity causes all points on the ellipse to be displaced toward 




Fig. 148. 

the crank end of the stroke. The resulting figure is of oval 
shape, in consequence of which the diagram is sometimes called 
the " Oval Diagram." 

(b) Owing to the effect of the angularity of the connecting 
rod, the piston displacement for similar events in the two strokes 
of a double-acting engine will not be equal if the laps on the 
two ends of the valves are the same. It is possible to " equal- 
ize " the cut-offs by using unequal steam laps, but in that case 
the conjugate events (admissions) are unequal. Similarly, the 
compressions can be " equalized " by using unequal exhaust 
laps, but then the releases will be unequal.* Equalization may 
also be accomplished by using special arrangements of rockers 
between eccentric rod and valve rod. This matter is discussed 
fully in most books especially devoted to valve gears, and will 
not be considered further here. 



152. Valve and Port Openings. For the rate at which the 
steam is supplied to the cylinder to be always equal to the rate 

* Except in the special case in which the exhaust lap would be zero if the 
" angularity " of the connecting rod were neglected. 



286 HEAT-POWER ENGINEERING 

at which volume is made available by the piston, the following 
expression must be satisfied : 

av = AV (273) 



in which 



Then 



a = area of passage (sq. in., usually); 
A = area of piston (same unit) ; 

V = velocity of steam (ft./min., usually); 

V = velocity of piston (same unit). 



a = AV -^ V (274) 

Valves are usually designed to have a maximum area of 
opening which corresponds to a velocity (v) of steam which has 
been found by experience to give satisfactory results. The 
maximum valve opening (a) is computed by using Eq. (274), in 
which V is the mean piston velocity (equal to 2 X stroke in 
feet X r.p.m.), and v has a value which in practice varies from 
6000 to 10,000 feet per minute, but is usually about 8000 feet 
per minute in simple engines. 

In designing the gear with single valve, it is generally only 
necessary to see that the steam opening of the valve is sufficiently 
large, for the exhaust opening will always be more than is re- 
quired because the exhaust lap is very much smaller than the 
steam lap. 

The width of the valve opening (used in constructing the valve 
diagrams) is of course equal to the area of opening divided by 
its length. This length is nearly always equal to the length of 
port across the cylinder. 

In case a simple valve is used, the area of the port in the 
cylinder should be sufficient for accommodating the exhaust 
steam, as the same passage is used for both the entering and 
the outgoing vapor. Its area may be determined from Eq. 
(274), using for the steam velocity (v) from 4500 to 7000 feet 
per minute, but about 6000 is usual in simple engines. This 
area is then more than is needed for the admission of steam. 

If the exhaust passage is separate from the steam passage, 
this latter can have area about equal to the maximum valve 
opening to steam. 

153. Cushioning the Reciprocating Parts, (a) First suppose 
there is no compression. Then when the piston approaches the 
end of its stroke the effective steam pressure and the inertia of 



THE VALVE GEARS OF STEAM ENGINES 287 

the reciprocating parts are both acting towards that end of the 
stroke, taking up the slack in the bearings of the reciprocating 
parts. Now, when the steam is admitted on the other side of 
the piston, the pressure on the bearings is reversed more or less 
suddenly. With reciprocating parts of small weight, and with 
high steam pressure, this reversal will be very sudden, and if 
there is much " play " in the bearings (and there must always 
be a little) the consequent impact or " hammering " will cause 
excessive stresses in the impinging parts, and will render the 
operation of the engine noisy. 

(b) One method of preventing the occurrence of these unde- 
sirable features is to make the weight of the reciprocating parts 
so great that their inertia will oppose the pressure of the enter- 
ing steam sufficiently to cause the play in the bearings to be 
taken up gradually, thus preventing impact. But as the inertia 
forces are free forces which tend to move the engine on its founda- 
tion, it is usually desirable to have them small, even when counter- 
balancing is attempted ; so this method is usually unsatisfactory. 

(c) Another method is to arrange the valve to open grad- 
ually, but this is accompanied by a more gradual cut-off, which is 
undesirable. 

(d) The best method is to gradually reverse the pressure on 
the bearings by introducing compression; then, when admission 
takes place, there is no play to be taken up and consequently no 
impact. 

It is possible to compute the inertia force of the reciprocating 
parts at the end of the stroke. Then in order to reverse the 
pressure on the bearings the steam pressure at the end of com- 
pression should equal or be greater than this inertia force plus 
the steam pressure on the other side of the piston. 

154. Early Valve Opening, (a) If steam is admitted just as 
the new stroke begins, the pressure will not rise immediately to 
the value in the steam pipe because (i) the valve opens grad- 
ually, (2) the clearance space must be filled, and (3) a large 
proportion of the entering steam is liquefied by cylinder conden- 
sation. Hence it is necessary to have the valve open before the 
commencement of the stroke; that is, the valve is given "lead." 
As the clearance volume is constant, the lead and crank angle at 
which opening occurs should be constant regardless of variations 



288 HEAT-POWER ENGINEERING 

in cut-off, if the speed of the engine is uniform. The higher the 
speed and the less the compression, the earlier should the opening 
of the valve occur. 

(b) In order to have the steam pressure drop to that of ex- 
haust by the time the end of the stroke is reached, the exhaust 
edge of the valve is given lead, causing " early release." As re- 
lease and compression are conjugate events, the fixing of one of 
these events determines the other. Often it is not possible to 
have both occur as desired, in which case a compromise must 
be made. 

155. Limitations of the Simple Valve. It is impracticable to 
have cut-off occur early in the stroke with the simple D-valve 

because, in order to obtain a satisfactory 
width of opening in such cases, it is found 
(i) that the valve and eccentric are ex- 
cessively large (and consequently the 
valve gear must work against great fric- 
tion and inertia forces), and (2) that the 
release and compression occur too early 
in the stroke. 

Fig. 149 is a Bilgram diagram for a 
valve cutting off at one-fourth stroke. 
If the scale is such that the maximum 

Fig. 149- . ^ ^ . • 1 V • 

openmg to steam is one mch, it is seen 
that all of the foregoing statements are true. The simple D-valve 
is not used with cut-offs much earlier than five-eighths stroke. 

Ordinarily, the best economy in a simple engine is obtained 
when cut-off is at about one-fourth stroke; hence the simple 
slide valve should not be used when economy is important. 

156. Special Types of Single Valves, (a) By increasing the 
length of the steam edge of the valve a reduction can be made 
in the port width, laps, travel, and eccentric throw; but there are 
practical limitations to increasing the length of this edge in the 
simple fiat valve. 

(b) Piston Valves, Fig. 150, which may be looked upon as 
flat valves rolled into cylindrical shape, may have greater length 
of edge (equal to the circumference) than the simple flat valve, 
without having prohibitive size. Fig. 150(a) shows an "exter- 
nal " piston valve; Fig. 150 (6) shows an " internal " one. 




THE VALVE GEARS OF STEAM ENGINES 




SECTION S> 
THROUGH X-X 

Fig. 150. — External and Internal Piston Valves. 

(c) Multiported Valves, in which there are two or more work- 
ing edges, are frequently used. Fig. 151 shows a "Double- 




SECTION B-BisECTlbN C-C 
Fig. 151. — Double-ported Marine Valves. 

ported Marine Valve," each end of which has two steam edges 
and two exhaust edges. 

(d) Some valves have auxiliary ports in them so arranged as 
to give multiported action. An example of this is the Allen or 
Trick Valve shown in Fig. 152. This valve 
has an auxiliary passage aa' and valve seat steam ^ <— 
so arranged that, as the valve moves to ^^*)^-^ 
the right in the figure, the edge / opens 
simultaneously with the main steam edge y. 
The exhaust is single-ported. 

Considering the valve as moving to the 
right, the phases of opening of the steam 
edge are: (i) ''Double-ported''' action while 
edges / and y open at the same rate. 
This continues until the auxiliary port a 

is wide open. (2) With movement continuing, Fig. 152 (6), the 
opening at y increases but that through a remains constant, 



l.M\ \ 



(a) 



■^»/ 



T~\ 



Vi 



if 



Fig. 152. — Allen Valve 




290 HEAT-POWER ENGINEERING 

i.e., the opening is "single-ported plus a constant.''^ This con- 
tinues until a' in Fig. 152 (c) becomes throttled by the exhaust 
edge of the valve seat. (3) As the opening at a' is then 
decreasing (as the valve continues to the right) at the same 
rate as that at edge y is increasing, the effective area remains 
" constant.'' (4) If the movement is sufficient to completely 
close a', the valve becomes " single-ported. '' Now if the valve 
returns to the left to close, the effective openings will decrease 
in the reverse order. 

The openings of the steam edge of an ordinary valve are 
shown by the sectioned part above the steam-lap line of the 

elliptical diagram in Fig. 139. 
This is also shown (somewhat 
distorted) by the light line in 
Fig- 153- The heavy Unes in 
this figure show the character 
p. J " of the openings when an Allen 

valve, like that just described, 
is used. Note that the smaller openings are affected more than 
the larger ones. 

Piston valves similarly arranged have been used (Armington- 
Sims valve). 

(e) The Sweet Valve shown in Fig. 154 is another valve hav- 
ing an auxiliary port. This valve is a rectangular piston valve 
which slides be'tween the valve seat and a "balance plate," 
which latter is supported by distance pieces so as to just clear 
the valve. The face of the balance plate is similar to the face 
of the valve seat. All sliding surfaces are scraped to give 
sufficient clearance for free movement of valve but not enough 
to permit of appreciable leakage of steam. The valve has 
separate auxiliary ports a at each end, which causes double- 
ported action through at least part of the opening of the 
valve. 

Referring to Fig. 155, it is seen that as the valve moves to 
the right the phases of opening of the steam edge are the same 
as those of the Allen valve; thus there is (i) " double opening,'' 
with 3; and /opening together; (2) " single-ported plus a constant," 
when / becomes greater than a; (3) " constant," when a is being 
closed by the exhaust edge of the valve seat at, same rate that y 
is opening; and (4) " single- ported," when a is entirely closed by 



THE VALVE GEARS OF STEAM ENGINES 291 

the exhaust edge. The areas during closure decrease in the 
reverse order. 

The auxiliary port, or another one, may be so arranged as to 
assist during the exhaust. 

(f) A combination of the Allen and Sweet arrangements 
gives quadruple openings (Woodbury valve) , and there are many 




Fig. 154. — Cylinder with Sweet Valve. 



Fig. iSS- 



Other forms of such valves. For further discussion see text- 
books on Valve Gears. 

(g) Valve Friction is undesirable, not only because of the 
waste of power it causes, but because it may disturb the action 
of the governor, if one is used. The whole back of the simple 
D-valve is subject to full steam pressure, while the larger part 
of the under side is exposed to the exhaust pressure. The un- 
balanced pressure causes excessive wear and friction loss at the 
rubbing surfaces. To reduce this unbalanced pressure, various 
schemes of " balancing " are used. The simplest is the use of 



292 



HEAT-POWER ENGINEERING 



a piston valve which is perfectly balanced except for its weight. 
The Sweet type of valve is practically the equivalent of the piston 
valve in this respect. Some valves have " balance or equilibrium 
rings " on their backs (like that shown in Fig. 156) so arranged 
that the area within the ring is subject to exhaust pressure and 
is about equal to the area subjected to exhaust pressure on the 
under side. However, in such cases there 
should always be enough unbalanced pres- 
sure to maintain steam-tightness between 
valve and seat. 

(h) In case there should be entrapped 
in the cylinder a quantity of water more 
than sufficient to fill the clearance space, 
some part of the engine would break dur- 
ing compression unless some means of 
relief were provided. Sometimes "Relief 
Valves," which are somewhat similar to 
boiler safety valves, are attached to the 
cylinder ends. Sometimes the slide valve 
itself offers this relief; for example, the 
simple slide valve, with or without balance 
rings, and valves (like the Sweet) with pressure plates can lift 
from their seats and thus give relief. In such cases there 
should be springs or other devices to return the valve and bal- 
ance ring, or plate, to its proper position after the cylinder has 
been relieved of the water. Piston valves offer no such relief 
themselves, and engines with this type of valve should be pro- 
vided with special relief valves or other similar device. 




Pig. 156. — ■ Valve with 
Balance Ring. 



157. Valve Gears for High-Speed Engines, (a) The high- 
speed engine was briefly described on page 245. It is fitted with 
a " shaft governor," which controls the point of cut-off by vary- 
ing the position of the eccentric with respect to the crank. 

(b) Simple engines of this type usually have cut-off occur at 
about one-fourth stroke when operating under " normal load." 
The " range of cut-off" is generally from zero to five-eighths or 
three-fourths stroke, and the " range of load " is from "friction 
load " to 50 or even 100 per cent overload. 

It was shown on page 288 that if a simple slide valve is used 
to give cut-off as early as one-fourth stroke, certain features will 



THE VALVE GEARS OF STEAM ENGINES 



293 



be introduced which are undesirable in the ordinary case. Two 
of these are early release and early compression. 

(c) It so happens, however, that these ph'enomena are de- 
sirable in a high-speed engine. The early release is advanta- 
geous, as it allows more perfect drop to back pressure in the 
short time available. The early compression assists in causing a 
gradual absorption of the inertia forces; and an excessive ter- 
minal pressure can be prevented by increasing the ratio between 
clearance volume and piston displacement. With a given 
clearance volume and piston area, this ratio can be made large 
by using a short stroke, and with high rotative speed a short 
stroke is desirable in order to keep the piston speed down to 
safe limits; hence what are faults in the ordinary case make the 
short-stroke high-speed engine possible. 

(d) The excessive size of the valve-gear parts, which ordinarily 
occurs when a valve is designed for an early cut-off, as was 
shown in Section 155, may be overcome by increasing the length 
of port, which calls for a narrower valve opening and a cor- 
responding reduction of the laps, travel, and size of the eccen- 
tric; and these in turn are accompanied by a decrease in the 
friction and wear of the valve gear. The greater length of port 
may be obtained by using a wide valve, a piston valve, or a 
multiported valve. 

With the type of valve gear which is used on this class of 
engine, the travel of the valve varies with the cut-offs, and 
the earlier the cut-offs the more restricted are the openings 
of the valve. The valves may be designed to have open- 
ings ample for the latest cut-offs, and to have auxiliary ports 
added in such a manner as to assist during the early openings 
only, and to have little or no effect on the wider openings. 
Examples of these various types of valves have already been 
given. 

Sometimes special arrangements of linkage are employed to 
give wide openings with small travel, as in the case of the 
"High-Speed Corliss " engine to be considered later. 

(e) The friction of the valve is undesirable, not only because 
it decreases the mechanical efficiency of the engine and causes 
(vear, but also because it disturbs the action of the shaft gover- 
nor. This latter is especially true if the governor is of the 
Inertia type. The governor is also affected by the inertia of 



294 



HEAT-POWER ENGINEERING 



the valve gear; hence high-speed engines use valves that are 
balanced and are of light weight. 

(f) In Fig. 157, which is a diagram of positions, i-j is one 
path, with respect to crank OP, over which the eccentric might 
be shifted by a shaft governor in adjusting the cut-off to meet 
the power demanded of the engine. When, in Fig. 157 (a), the 
eccentric is at i (with throw O-i and angle of advance ai) the 
cut-off is at about three-fourths stroke, for when the eccentric 
has rotated in the direction of the arrow to Ci (displacement 



■<■ btroke 




Fig. 157. — Diagram of Positions. 
equal to steam lap) the crank pin is at Ci] when, in Fig. 157 (b), 
the eccentric is at 2 (with throw O-2 and angle of advance 0:2) 
the cut-oflf is about one-half stroke, for when the eccentric is 
at C2 the crank pin is at G; and when the eccentric is at J, 
diametrically opposite the crank, the cut-off is at C3. In this case 
the path i-j is so selected that it will coincide with Lai when 
the crank is in position OAi; hence the crank-pin positions 
(Ai, A2, and A3) for the admissions corresponding to all cut-offs 
will coincide, that is, the admission is constant. 

With crank at OP, the horizontal distance between the eccen- 
tric and the steam-lap line aiCi is the lead. From the figure it 
is seen that Lead2 is less than Leadi, and that as the eccentric 
is shifted to give earlier cut-off the lead becomes less. 

The figure also shows that when the eccentric throw is 0-J 
the maximum valve opening is LMi, when the throw is O-2 the 
maximum opening is LM2, and with 0~j this opening is L-j. 
Thus the maximum openings decrease as the cut-off is made to 



THE VALVE GEARS OF STEAM ENGINES 



^95 



occur earlier. The valves are therefore usually designed to 
have proper opening at latest cut-off when operating as a single- 
ported valve and to be multiported when early cut-offs occur. 

If the exhaust-lap line is added to the diagram of positions, 
Fig- 157. and the crank positions are determined for exhaust 
events corresponding to the different points of cut-off, it will be 
found that as cut-off is made to occur earlier the release and 
compression are also made earlier. Thus with early cut-off 




Fig. 158. 



Fig- 159- 



there is greater compression than with late cut-off. Fig. 158 
shows how these events vary and affect the form of the ideal 
indicator diagram, and Fig. 159 is an actual diagram obtained 
from a high-speed engine. 

From the foregoing it is seen that the following general state- 
ment can be made: As the eccentric is shifted from the outer to 
the inner position, cut-off, release, and compression are made to 
occur earlier and the maximum opening is decreased. 




Fig. 160. Paths of Swinging Eccentric. Fig. 161. 

Instead of shifting the eccentric over a straight path, it can be 
swung about a pivot in the governor case or flywheel. When an 
inertia governor (Fig. 130) is used with external valve, the eccen- 
tric center will be moved over a circular path, as in Fig. 160, with 



296 



HEAT-POWER ENGINEERING 



pivot opposite the crank. When the ordinary centrifugal gover- 
nor is used, the eccentric may be pivoted on either side of the 
shaft with respect to crank, hence its path may be that in Fig. 
160 or that in Fig. 161. These curved paths approximate the 
straight one in Fig. 157. The admission will vary as the eccen- 
tric position is changed, and the character of the variation depends 
on the curvature of the path. 

(g) The various valve-gear diagrams can be constructed in 
the usual manner, taking each position of the eccentric inde- 




Fig. 162. — Valve Diagrams for Variable Eccentric Valve Gear. 

pendently. The diagrams for the different eccentric positions 
may be drawn separately, but usually they are superimposed on 
one another, as in Fig. 162, which corresponds to Fig. 160. 

(h) At any one cut-off the valve events can be equalized in 
the manner mentioned in Section 151 (b). In some cases it is 



THE VALVE GEARS OF STEAM ENGINES 297 

possible to approximate the equalization in all positions of the 
eccentric by using a special arrangement of rocker arm or guide 
for the eccentric-rod pin. 

158. General Characteristics of Independent Cut-off Gears. 

(a) If an engine operates at a constant speed, as most engines do, 
it is desirable to have the admission, compression, and release 
remain constant, no matter how the cut-off varies. It has been 
seen that the simple valve with shifting eccentric does not give 
this desired constancy of all these events, nor does it give suf- 
ficient opening and sharp closure when cut-off is early in the 
stroke. If, however, instead of a single valve, two or more are 
used, with two independent sets of valve gear, it is possible to 
avoid some or all of these difficulties. Owing to the complications 
and extra expense involved with such arrangements, they are not 
often used on the small high-speed types of engines. They are 
quite common on larger and longer stroke, medium speed engines. 
(b) In general the gear having the two valves may be ar- 
ranged in either of two ways: (i) Each valve may control one 
pair of conjugate events; thus, one valve, having a fixed eccen- 
tric, may operate the release and compression, while the other 
valve takes care of the admission and cut-off, the latter event 
being changed by shifting the eccentric by a shaft governor, as 
in the case of the valve gear used on high-speed engines. In 
this case, separate valve diagrams would be drawn for each pair 
of conjugate events; that for the steam events would be con- 
structed the same as for the simple-shifting eccentric gear ; that 
for the exhaust events would be constructed the same as for 
any case in which the crank positions for the opening and clos- 
ing of the exhaust edge are given, together with the maximum 
width of opening desired. This arrangement will not be con- 
sidered further. (2) In the other arrangement of the gear, one 
valve, which will be termed the main valve, controls the admis- 
sion, compression, and release, and is driven by a fixed eccentric 
(" main eccentric "). The other valve operates the cut-off only, 
and will be called the cut-off valve. It is an intercepting valve, 
being located between the main valve and the source of steam 
supply. It may slide on a separate valve seat, or it may ride on 
the back of the main valve, in which case it is called a " riding " 
cut-off valve. 



298 HEAT-POWER ENGINEERING 

The variation in cut-off may be accomplished in three ways: 
(a) by changing the lap of the cut-off valve, (b) by changing the 
position of the cut-off eccentric with respect to the crank, and 
(c) by a combination of (a) and (b) . 

The range of cut-off on medium-speed engines is usually from 
zero to five-eighths or three-fourths stroke. Under normal load 
simple engines usually cut-off at about one-fourth stroke. 

(c) In all the gears having a cut-off valve of the intercepting 
type, the main valve or valves (operated by the main eccentric) 
control the admission, release, and compression. 

Referring to Fig. 144 it is seen that the line OQ bisects the 
angle formed between OR and OK produced; hence, in order to 
determine [the proportions of the main valve and its eccentric, 
proceed as follows: 

The two conjugate events (R and K), which can be decided 
upon initially, fix the angle of advance of the main eccentric, for, 
in the Bilgram diagram. Fig. 163, OQi must bisect the angle 



Max. 
Opening 



Fig. 163. Fig. 164. 

between R and K (produced). After drawing the lead line L, and 
the arc W for maximum opening, the steam lap is determined 
by drawing the lap circle tangent to W and L in the figure, the 
center, Q, being on OQi. Having located Q, the exhaust-lap cir- 
cles can then be drawn. The diagram is now complete and all 
dimensions for the valve and eccentric have been found. The 
cut-off of the main valve is unimportant, provided it is at least 
as great as the latest given by the cut-off valve. Compression, 
of course, can be equalized by using unequal exhaust laps. 

The diagram of openings of the main valve, which is that 
part of the elliptical diagram which lies above the steam lap, 
S.L., (for the H.E. of the valve), is shown in Fig. 164. 

(d) In all valve gears in which there is a separate cut-off 



THE VALVE GEARS OF STEAM ENGINES 



299 



valve it is necessary that this valve open before the main valve 
does, as the latter controls the admission. To provide for this, it 
is necessary in many instances to have negative lap on the cut-off 
valve and large angle of advance, a , of the cut-off eccentric {a 
may even be greater than 180 degrees in some instances). 

In the general case the constructions of the various valve 
diagrams for negative lap and large angle of advance are identical 




Fig. 165. 



with those previously described; in each case the angle of ad- 
vance is located in exactly the same manner, and the negative 
lap is laid off opposite the positive lap; the openings are then 
equal to the displacement plus the negative lap, and the closures 
equal the displacement minus this lap. With negative lap the 
valve when central is open, hence closure must occur after the 
central position has been passed, and opening takes place before 
that position is reached. Figs. 165 (h) to (e) show the various 
valve diagrams for angle of advance greater than 90 degrees, 
and Fig. 165 (a) gives the actual position of the eccentric with 



300 HEAT-POWER ENGINEERING 

respect to the crank when the latter is on dead center. The 
lengths of the section lines show the widths of valve openings. 

The generating point in the elliptical diagram will move 
around the ellipse in a counter-clockwise direction if the angle 
of advance is greater than 90 degrees, as it is in Fig. 165. As 
before, the part of the elliptical diagram lying above the steam- 
lap line constitutes a diagram of openings. 

The cut-offs at one point in the stroke can be equalized by 
using unequal laps. 

(e) Referring to Fig. 165 (e), it is seen that the cut-off can be 
varied either (i) by altering the size of the lap circle (which may 
even be made positive), or (2) by changing the angle of advance, 
a. Both methods are used in practice. 

A shaft governor may be used to automatically change the 
angle of advance by turning the cut-off eccentric about the 
center of the shaft on which it is loosely mounted. 

159. Independent Cut-off Valve with Stationary Seat. Fig. 
166 shows diagrammatically an arrangement with cut-off valve 
C riding on an independent valve seat 
between the main valve M and the steam 
n/ J ^ 1 ^ — ^Ij- pipe. The main valve is driven by a fixed 
eccentric. It controls the admission, re- 
lease, and compression, and is designed in 
the manner outlined in Section 158 (c). 



: 



JT^TS^- 



Fig. 166. The cut-off valve is driven by an inde- 

pendent eccentric and controls only the 
one event. The cut-off can be changed in either of two ways 
already mentioned. 

Case I. — The lap of the cut-off valve may be altered by any 
of the following methods: 

(i) The valve may be in two parts, mounted on the valve 
stem with R.H. and L.H. threads respectively. By turning the 
stem, the distance between the ends, and consequently the laps, 
can be varied. With this arrangement, as in Fig. 167, the ad- 
justment is made by hand, and the point of cut-off for the setting 
can be read on the indicator, which is moved by a nonrotating nut 
on the valve stem. It is difficult to arrange a governor to make 
the adjustment with this arrangement, as several revolutions of the 
valve stem are required to accomplish the full range of cut-off. 



THE VALVE GEARS OF STEAM ENGINES 



301 




Fig. 167. 

(2) Fig. 168 shows the back of another arrangement in which 
the edges of the valve and ports are obUque. On the back of 
the valve is a rack with which a pinion, on the valve stem, 
engages. By turning the stem the valve may be raised or 
lowered (as viewed in the figure), thus changing the distance be- 
tween its edge and that of the port. 



;<. Valv 


e M 


V" 


.^7 


^i 


^M. 




n ^ifrNeg. 


Lap 




Fig. i( 



Fig. 169. 



(3) Fig- 169 shows a somewhat similar arrangement, except 
that the valve face and seat are cylindrical surfaces. The valve 
is fastened to the stem, so that by turning the latter the lap is 
changed. 

The arrangements shown in Figs. 168 and 169 can be controlled 
by a fly-ball governor, which can be connected to an arm on the 
valve stem. 

Case II. — The angle of advance may be changed, as in Fig. 
, 170, in which M is the main eccentric, o, J and f are the positions 
of the cut-off eccentric for those cut-offs, X is the " range angle " 
through which the governor has to turn the eccentric on the 
shaft, ao' is the maximum angle of advance of the cut-off eccentric, 
and aa' is that for three-fourths cut-off. 

Fig. 171 shows for this case the diagram of openings of the 
cut-off valve (dotted lines) superimposed on that for the main 
valve (heavy lines), and the sectioning shows the effective open- 
ing from the time of admission of the main valve to the closure 
of the cut-off valve at one-fourth stroke. 

The arrangement of valves shown in Fig. 166 is not satisfac- 
tory, as with early cut-offs the space beyond the end of the main. 



302 



HEAT-POWER ENGINEERING 




Fig. 171. 



valve is clearance space during the part of the expansion preced- 
ing the closure of the main valve. 

160. Riding Cut-off Valves, (a) Instead of having a separate 
seat for the cut-off valve, this valve may ride directly on the 
back of the main valve (or within it, if piston valves are used) and 
perform its functions with respect to a port in that valve. There 
are several such arrangements possible. One, the Buckeye 
Gear, is in effect the exact equivalent of the arrangement de- 
scribed as Case II above. 

The arrangement of valves in this gear is given in Fig. 172, 
both valves being shown central with respect to the ports. The 



<Exi, 



1 ^Sieam'Lap 
■I-ir- kI~^-1'"T^<''^ CO Lap 




Fig. 172. 



cut-off valve has negative lap equal to the amount it is open in 
the figure with respect to the main valve. The main valve is a 
box filled with live steam, practically a reciprocating steam 
chest. It is an " internal " valve, taking steam from the inside 
and exhausting at the ends. The cut-off valve rides inside the 



THE VALVE GEARS OF STEAM ENGINES 303 

main valve and is "external"; its negative lap is of constant 
amount. Its valve stem passes through that for the main valve, 
the latter being hollow. 

The main valve is driven by a fixed eccentric, and controls 
admission, release, and compression. The cut-off valve is driven 
by an eccentric which is controlled by a shaft governor which 
turns the eccentric about the center of the shaft, thus varying 
the angle of advance, a', as in Fig. 170. 

(b) The arrangement of the rockers which guide the eccentric- 
rod ends is shown in Fig. 173. The main rocker ab is pivoted at b 



^ 



J5k 

1 To M. Eoc 



^^^^M 



Fig. 173. 

to the frame of the engine. The cut-off rocker cd is pivoted at 
Its middle e to the middle of the main rocker. With this special 
arrangement of rockers, it is seen that the displacement (5) of the 
center of the cut-off valve with respect to the center of the 
main valve is given by the distance between a and c, which is 
the same as that between b and d. Evidently, then, the motion 
of the cut-ofT valve with respect to the main valve is the same 
as that of c with respect to a, or opposite to that of d with re- 
spect to b. Since & is a fixed point, it follows that the motion of 
the cut-off valve with respect to the main valve is the same as that 
of a simple valve with respect to a fixed seat. The distance the 
cut-off valve travels with respect to the main valve remains 
constant, no matter how the cut-ofif and phase relations of the 
two valves are altered by changing the angle of advance of 
the cut-ofif eccentric. 

Thus this arrangement is equivalent to Case II of Section 159, 
but avoids its faults. 

(c) In other " riding cut-off " gears, this peculiar arrange- 
ment of rockers of the Buckeye gear is not used, but both 
valves receive motion direct from their respective eccentrics. 
The general arrangement of the valves is shown in Fig. 174, in 
which both valves are external. The main valve has a false 



304 



HEAT-POWER ENGINEERING 



end B, the only purpose of which is to provide an edge F, with 
respect to which the cut-off valve opens or closes. Each valve 
is driven by its own eccentric, the location of which is shown in 




Fig. 174. 



a{;>^ /Y"Maiu Ecc. 



OjSr^ — ilc.O.-Ecc. 
r]'- Relative Ecc. 



Fig- 175- 



Fig. 175. The main valve controls the admission, release, and 
compression, and is designed as in (c) of Section 158. To 
analyze the action of the cut-off valve, its motion with respect 
to the main valve must be considered. 

(d) As the crank revolves, not only do the eccentrics rotate 
about the center of the shaft, but they rotate about each other. 
That this last statement is true can be seen by turning Fig. 
175 about 0, and it will be noticed that, at the same time, the 
cut-off eccentric rotates about the main eccentric and in the 
same direction as that in which the crank turns. Evidently, 
then, the motion of the cut-off valve with respect to the main valve 
is produced by the rotation of the cut-off eccentric about the main 
eccentric; hence, this motion is equivalent to that which a simple 
valve would have, with respect to a fixed seat, if driven by an eccen- 
tric having throw equal to the distance between the eccentric centers 
(Fig. 175) and with angle of advance equal to 6. This imaginary 
eccentric will be called the " relative eccentric " R. Thus, to 
analyze the action of the cut-off valve with respect to the main 
valve (its moving seat), the position of the relative eccentric 
must first be determined, after which the valve diagrams would 
be constructed in the usual manner, but using the throw and 
angle of advance of this eccentric. 

(e) The Meyer Valve Gear has the same arrangement of 
valves as that shown in Fig 174. The cut-off eccentric usually 
has a 90-degree angle of advance, that is, it is located opposite 
the crank. The cut-off is varied by changing the lap of the 
valve by the method shown in Fig. 167. 

(f) The Russell Valve Gear is similar in character to Figs. 
174 and 175, but the cut-off is altered by changing the position 



THE VALVE GEARS OF STEAM ENGINES 



305 



of the cut-ofif eccentric. This adjustment is made by a shaft 
governor which turns the eccentric on the shaft to vary the angle 
of advance. 




Fig. 176. 




Fig. 177. 

The valves are shown in Figs. 176 and 177. The main valve 
operates the admission only. The exhaust is controlled by sepa- 
rate triple-ported valves of the Corliss type shown in Fig. 177. 



3o6 



HEAT-POWER ENGINEERING 



The cut-off valve is made triple-ported, as is its seat on the back 
of the main valve. The arrangement of eccentrics is similar to 
that shown in Fig. 170. 

(g) The Mclntosh-Seymour Gear has separate main, cut-off, 
and exhaust valves, of the "gridiron" type, working across 
the cylinder, as shown in the section in Fig. 178. These six 




Fig. 178. 

valves are driven by arrangements of rockers and toggles in the 
linkage, which distort the movements, so that after the valves 
are closed they have little motion; hence the friction and wear 
are reduced to a minimum. 

The main valve receives its motion from a fixed eccentric, 
and the cut-off valve is driven by an eccentric which is turned 
about the shaft by a shaft governor to adjust the cut-off. Fig. 
100 (p. 247) shows the general arrangement of the valve gear 
and the rocker shafts, which latter are given an oscillatory 
motion by the eccentrics acting through bell cranks. The 
arrangement of eccentrics is similar to Fig. 170. 





Fig. 179. 



Fig. 180. 



Fig. 179 is the distorted elliptical diagram for the main valve, 
with the opening diagram shown by bold lines. Superimposed on 



THE VALVE GEARS OF STEAM ENGINES 



\oi 



the latter are lines showing the closure of the cut-off valve. Fig. 
1 80 gives the distorted elliptical diagram for the exhaust valve. 
It is seen that the valve movements after closure are much less 
than with ordinary valve gears. 

(h) There are many other possible arrangements of riding 
cut-off gears, a great number of which are in actual use. 

161. Gears with Oscillating Valves, (a) Instead of having 
the slide valve flat, it may have a curved face, as in Fig. 181, in 
which case the valve oscillates about center 0' . The displace- 
ment X of the eccentric-rod pin U from the Y-axis is always 
equal to that of the eccentric with respect to the vertical axis 
through the shaft. This valve is substantially equivalent to 
the ordinary flat D- valve, and would be designed or analyzed in 




Fig. 181. — Oscillating Valve. Fig. 182. 

the same manner, using the same valve diagrams. These dia- 
grams show the true positions of the crank for all events; but 
the laps, displacements, and openings are chordal, that is, would 
be measured as chords instead of as arcs. 

(b) This arrangement of valve introduces very long steam 
passages, extending from the center to the ends of the cylinder, 
and this is not conducive to economical performance, as has 
already been seen. 

(c) A better arrangement is one in which there are four 
oscillating valves, as in Fig. 182, each of which performs the 
single function of one of the four edges of the single valve. In 
the figure the outer edges of the two upper valves control the 
steam events, and the inner edges of the lower valves operate 
the exhaust events. The other edges of the valves perform no 
function. The chordal laps would be the same as in the case of 
the single valve of Fig. 181. The valves shown in Fig. 182 are 
of the " Corliss " type. With this arrangement the steam and 
exhaust passages are very short and direct, thus the clearance 
volume and surfaces are relatively small. 



3o8 



HEAT-POWER ENGINEERING 



(d) All four valves may be driven by the single variable eccen- 
tric with shaft governor, as is common with high-speed engines. 
It is better, however, to connect the steam valves in this manner, 
and to drive the exhaust valves by a separate fixed eccentric, so 
that release and compression will remain constant. 

(e) One fault of most valve gears is that the valve has large 
movement after it has closed. To reduce wear and friction, the 
movement should cease as soon as the overlapping is sufficient 
to prevent leakage. Also, it is desirable to have more rapid 
fnovement of the valve after it opens than is obtained with the 

Imaginary I 

Equivalent Eccentric_.J>. A 




Fig. 183. 



simple gear. Both results can be effected by using links and 
rockers so arranged as to give the valve the desired motion. 
One such arrangement is shown in the upper right-hand corner 
of Fig. 183. Engines using this type of gear may be called High- 
Speed Corliss Valve Engines, or positive cut-off Corliss engines. 

(f) At the left of Fig. 183, the edge s of the steam valve is 
shown even with the port edge with which it opens or closes. 
Let g' be the desired (small) angular movement after closure, 
and / be the (large) angle after opening. The steam arm o^a', 
which moves the valve, will swing through the same angles as 
the valve; thus g and / are respectively equal g' and /'. The 



THE VALVE GEARS OF STEAM ENGINES 



309 



pin position a' for admission (motion to right) of course coin- 
cides with c' for cut-off (motion to left). 

Starting at the right of the figure, Ea is the eccentric position 
for admission; Em, that for maximum opening; Ec that for cut- 
off; and En is for extreme closure. The similarly subscripted 
positions of pins H and / on the rocker arm, the positions A, 
M, C, and N of the reach-rod pin, and a,m,c, and n of the steam 
pin, all respectively correspond with these eccentric positions. 
In each case the position for admission (motion to the right) 
coincides with the position for cut-off (motion to the left). It 
will be seen that the angular movement am of the steam pin 
for opening is smaller than that for closure en, which is just 
contrary to what is desired for the valve movement. However, 
it is possible to locate the steam pin on the wrist plate in such 
position, and to use such a length of steam rod, that the steam 
arm moves through angles n'c' and a'm' respectively when the 
steam pin moves through angles nc and am, and thus to ac- 
complish the desired result. With such arrangement the dis- 
tances nn', aa' , and mm' must of course all be equal, since they 
represent the length of the steam rod. 

The exhaust valve motion can be similarly distorted so as to 
be small after closure and large after release. The arrangement 
for the crank end of the cylinder is identical except reversed. 

(g) There are many other arrangements of linkage used for 
high-speed Corliss valve engines. Some involve the use of a 
separate fixed eccentric to drive the exhaust valves and thus 
obtain constant release and compression. 





Fig. 184. Fig. 186. 

(h) In Fig. 184 is given the distorted elliptical diagram for the 
steam valve of one gear of this high-speed Corliss type. 

(i) The Trip-Cut-off Corliss Engine with Single Eccentric. 
Fig. 185 is similar to the arrangement just discussed, except that 
the eccentric is fixed and the cut-off is operated by a tripping 



3IO 



HEAT-POWER ENGINEERING 




THE VALVE GEARS OF STEAM ENGINES 



311 



device positioned by a governor of the fly-ball type. The type 
of steam valve used is shown in Fig. 186; and the bonnet for the 
head-end steam valve, and the part of the gear which it supports, 
are illustrated in Fig. 187 (a) . The names of these parts are given 
in Fig. 187 (b). The left arm A of the bell crank carries a hook C 




Fig. 187. — Steam Gear — Corliss Engine. 

which engages with the steam arm on the valve stem. If the 
hook remains latched, the motion which the bell-crank arm B 
obtains from the wrist plate by means of the steam rod is 
transmitted directly to the valve, and the case is identical with 
that discussed in (f) of this section. In these engines, however, 
the governor controls the position of the knock-off cam E, which 
has a definite position corresponding to each different cut-off. 
As the bell crank is moved clockwise, the hook turns the steam 
arm and opens the valve (as in Fig. 183). This continues until 
the part D of the hook comes in contact 
with the stationary knock- ofif cam E, 
when" the hook becomes disengaged from 
the steam arm, which is then returned 
to its lowest position by the dash pot, 
thus closing the valve. 

(j) The simple elements of the dash pot 
are shown in Fig. 188. When the steam 
valve is opened the plunger is raised and 
a vacuum is formed at V. After the hook 
has been tripped this vacuum causes the 
descent of the plunger and closure of the 
steam valve. The fall is stopped by the air cushion which is formed 
between C and C and which is adjusted by the cushion valve. 




Fig. 188. — Dash Pot. 



312 



HEAT-POWER ENGINEERING 



(k) Fig. 189 shows the distorted elliptical diagram for the 
steam valve. With the trip occurring at t, the cut-off is at c. 
As the valve cannot close instantaneously, tc will slope somewhat. 
A similar diagram for the exhaust valve is given in Fig. 190. 

T ^Latest Trip OverTravel| 




Fig. 189. 



Fig. 190. 



In connection with Fig. 187, it will be noticed that the trip of 
the head-end steam valve occurs when the hook end D comes 
in contact with the stationary cam E, while the hook and bell 
crank are still moving to the right (that is, before the eccentric has 
reached the R. H. dead center) ; and that if, when the eccentric 
arrives at this position, the trip has not taken place {E being 
too far to the right), it will not take place at all, and cut-off will 
occur at C in Fig. 189 instead of at C. 

(1) The angle of advance is fixed by the release and com- 
pression, as in the case of the main valve of the riding cut-ofif 
gears (Fig. 163). It is in no way dependent on the other events, 
for with crank on dead center the steam rod can be adjusted to 
give the valve the proper lead, and cut- 
off is controlled hy the knock-off cam 
independently of the eccentric. 

If E in Fig. 191 is the eccentric po- 
sition for latest trip, the crank pin is 
then at T and the piston at C. As, 
however, some time must elapse before 
the valve is closed, cut-off will occur 
^S' -^^i- when the piston has reached some po- 

sition D, which is usually at about 0.4 stroke. Thus with an 
ordinary single eccentric Corliss gear the latest cut-off possible is 
about 0.4 stroke, and this is accomplished only by using the 
smallest angle of advance that will give the proper release and 
compression. 

(m) There are many other arrangements of valves, of trip 
gear, of wrist-plate linkage, and of dash pot, but all operate in 




THE VALVE GEARS OF STEAM ENGINES 



313 



a manner similar to that described. The valves are frequently 
double- or multiple-ported. 

(n) One of the faults of this gear is that a failure of governor 
belt stops the governor and lets the weights drop to the lowest 
position, thus advancing the cut-off to the latest point. The 
power then developed is greater than that absorbed, and the 
engine will "run away" and be demolished, unless stopped by 
hand or by some safety device. 

One safety device consists of a " safety cam " 5 in Fig. 187 
which prevents the hook engaging with the steam arm when 
the governor occupies its lowest position. Some engines have 
auxiliary fly-ball governors which will close the throttle valve 
when the speed becomes unsafe. There are many other forms 
of safety devices in use. 

(0) The limitation of the latest cut-off can be avoided by 
using the Two-Eccentric Corliss Gear, in which one eccentric 
drives a wrist plate for the exhaust 
valves, and another one actuates the 
steam wrist plate. Fig. 192 shows the 
arrangement of eccentrics, with crank- 
on dead center. The angle jS between 
the crank and steam eccentric fixes the 
latest cut-off, but with this arrangement, 
since the exhaust valves are driven in- 
dependently, it may be made any value 
within limits. The angle used in the 
figure permits of cut-off as late as three-fourths stroke as is seen 
from the extreme (dotted) position. 

Late cut-off can also be obtained by using a moving knock-off 
cam which may be oscillated either by a separate small eccentric at 
about 90 degrees with the main eccentric, or by the sidewise motion 
of the eccentric rod, which is 90 degrees out of phase with the longi- 
tudinal movement. With such arrangement the knock-off cam 
overtakes the hook and releases it even after the main eccentric 
has rotated a considerable angle beyond the dead-center position. 

(p) The rotative speed of trip-cut-off Corliss gears must be 
relatively low, for otherwise the hook gear becomes uncertain in 
action. Speeds above 120 r.p.m. are seldom used, and generally 
they are considerably less. Hence engines using this type of 
gear are commonly classified as " low-speed." 




Fig. 192. 



314 



HEAT-POWER ENGINEERING 



(q) There are several trip-cut-off gears which have gridiron 
valves working across the cylinder either horizontally (some- 
what similar in arrangement to Fig. 178) or vertically. Trip- 
cut-off gears are also used with poppet valves (Section 164). 

162. Link Gears, (a) The valve gear most commonly used 
on engines which are reversed is the Stephenson Link Gear, one 

arrangement of which is shown 
semi-diagrammatically in Fig. 
193. The illustration is for a 
vertical engine with cylinder 
above, but the arrangement for 
a horizontal engine would be 
identical except for the position 
of the longitudinal axis. 

(b) The eccentrics are ar- 
ranged as in Fig. 194, with the 
"forward eccentric," /, placed 
90 degrees plus angle of advance 




Fig. 193. — Stephenson Link Gear. 




ahead of the crank in the forward direction of rotation, and the 
" backing eccentric," b, at the same angle in the opposite direction. 
If the valve receives all its motion from eccentric /, the rotation 
will be forward (clockwise in this case) ; if from b, it will be back- 
ward (counter-clockwise) . 

In Fig. 193 it is seen that the forks at the ends of the two 
eccentric rods are connected by a " link " (whence the name of 
this type of gear), different points of which may be brought 
opposite the " link block " on the end of the valve stem, by 
turning the " reverse " shaft. The illustration shows the for- 
ward end opposite (in "full gear" forward), hence the valve is 
receiving all its motion from the forward eccentric and conse- 



THE VALVE GEARS OF STEAM ENGINES 315 

quently rotates forward with latest cut-off possible. If the other 
end of the link is brought opposite the link block ("full gear" back- 
ing), the engine would operate backward at maximum cut-off. 

With the middle of the link opposite (" mid-gear "), the valve 
receives motion equally from both eccentrics; and the valve 
will open an amount equal to the lead and close immediately, 
the cut-off being practically at zero stroke. 

If the link is shifted from mid-gear toward the forward end, 
the valve will still receive motion from both eccentrics, but the 
major part will be from the forward eccentric. As the forward 
end of the link is shifted nearer the link block, the width of 
valve opening is increased and the cut-off is advanced in a man- 
ner quite similar to that in the gear with single variable eccentric, 
Figs. 160 and 161, when the eccentric is moved from inner posi- 
tion 3 outward towards /. In fact, an approximate analysis of 
the Stephenson link gear can be made by considering the valve 
as driven by a single swinging eccentric with a radius of path R 
which can be computed by McFarlane-Gray's formula: 

„ _ distance between eccentric centers X length of ecc. rod , . 
2 X distance between eccentric-rod pins 

(c) If, with the crank P pointing away from the cylinder, the 
rods are not crossed, as in Figs. 193 and 195 (a), the arrangement 
is termed " open rod." In this case the path of the equivalent 
single eccentric is feb with radius R. If, with crank in the same 
position, the rods are crossed, as in Fig. 195 (&), it is a "cross- 
rod " linkage, and the path of the equivalent eccentric is feh* 

For any link position, the equivalent eccentric occupies the same 
relative position on its path/6 as the link block on the link FB. 
It is seen that the open-rod linkage gives increasing lead as the 
cut-off is decreased, whereas the reverse occurs with crossed 
rods. From Eq. (275) it is seen that using longer eccentric 
rods increases R, thus making the path straighter and the lead 
less variable. To have the lead vary equally at the two ends of 
the valve, the radius of the link arc must equal the length from 
eccentric center to eccentric-rod pin, in the arrangement shown. 

* Note that when the crank has rotated 180 degrees the rods are crossed in the 
" open-rod " arrangement and open in the " crossed-rod " gear. In classifying the 
arrangement the crank must point away from the cylinder. 



3i6 



HEAT-POWER ENGINEERING 





1 


A 


V 


I Open 


Rods / 


uU Getir I ^^ 


/ 


Lead^.J/^ 


?^& 


4p^/ \ 


r^' r 






P 


l/(a) 




Full Gear 
Lead \ ^ j, l^ 



A (6) 



Fig- 195- 



(d) The link shown in Fig. 193 is of the " double-bar " type. 
There are many other arrangements: some have the eccentric- 
rod pins offset from the link; on some the suspension-rod pin is 
located at the middle of the link arc; on others, between the 
middle and the end. The modifications introduced in such cases 
cannot be considered here. 

(e) For the method of making an exact analysis of the action 
of the valve operated by a Stephenson link see textbooks on 
valve gears. 

(f) In the Gooch Link Gear, Fig. 196, the "radius rod," 
instead of the link, is shifted to change the cut-off. As the link 
radius equals the length of the radius rod, there is no move- 
ment of the valve if the adjustment is made when the crank is 
on dead center, as in the figure; hence the lead is constant. 
Line Vf is the path of the equivalent single variable eccentric, 
and h'hO is a right angle. 

(g) The Allan Link Gear shown in Fig. 197 has a straight 
link. The link and the radius rod are shifted in opposite direc- 
tions in such manner that the valve is not moved when crank 
is on dead center, hence the lead is constant. The path of the 



THE VALVE GEARS OF STEAM ENGINES 



317 




Fig. 196. — Gooch Link Gear. 



Fig. 197. — Allan Link Gear. 



equivalent single eccentric is similar to that in the Gooch link- 
•age. 

(h) The Porter- Allen Gear shown in Fig. 198 has a link which 
is consolidated with the eccentric strap and is guided at A along 




Steii). 



(a) 
Fig. 198. — Porter-Allen Gear. 

the center line of the engine. The throw OM of the eccentric 
equals lap plus lead, thus, in the position shown, the head end of 
the valve is open to lead. As the eccentric rotates from this 
position the tilting of the link increases the opening, which later 
is decreased by the translatory motion of the link. At {a) in 
the figure, with link block at F, maximum opening occurs at 
crank position 2 and cut-off at j. With link block in a lower 
position, there would be less opening and earlier closure, the 
lead remaining the same, however. 

Motion satisfactory for exhaust valves can be obtained from 
some point such as E. 

163. Radial Valve Gears, (a) In vertical multicylinder ma- 
rine engines using link gears, the valves are usually located per- 



3i8 



HEAT-POWER ENGINEERING 



pendicularly over the shaft, and some or all of them lie between 
the cylinders and thus lengthen the engine. It is true that by 
using rocker arms the valves might be placed at the side, but that 
arrangement of mechanism has certain disadvantages, and even 
then the eccentrics prevent, to a certain extent, the shortening of 
the engine. 

Using the type of valve gears known as " radial gears " necessi- 
tates placing the valves on the side of the engine. In most of the 
gears of this type a single eccentric is used and in some the eccen- 
trics are dispensed with altogether. With this type of gear the 
engine can be made to occupy less space than with link gears. 

There are a great many kinds of radial gears; only the most 
important will be described. 

(b) The Marshall Type of Gear, which is shown in Fig. 199, 
uses a single eccentric, either at 0° or 180° with the crank. 




Compr^iaV' 



Fig. 199. — Marshall Type of Radial Gear. 



The point a on the eccentric rod Eab is guided along path Gg* 
The end b traces the oval figure shown, and its positions are 
numbered to correspond with those of the eccentric and crank. 
The motion which the valve receives through the rod be is prac- 
tically the same as that obtained from an eccentric. By chang- 
ing the inclination of the guide Gg the oval is changed, the 

* The Hackworth gear has a straight guide. 



THE VALVE GEARS OF STEAM ENGINES 



319 



amount of opening is altered, and the cut-off is varied. A re- 
versal of the inclination, as G'g' reverses the engine. The pin b 
may either be located as shown or it may be between E and a. 

(c) If any point in a linkage moves in phase with the crank 
and describes a path that is approximately circular, a pin located 
at that point can be used instead of the eccentric to give the 
valve the motion equivalent to that obtained with the Marshall 







Fig. 200. — Joy Radial Gear 

In the Joy Gear, shown in Fig. 200, ac 
is a link with one end attached to the con- 
necting rod and the other end to the sus- 
pension link /c. The point E moves in 
a path which may be substituted for the p 
eccentric circle. The rest of the linkage 
resembles the Marshall in character and 
performance. 

(d) If, in Fig. 201, the harmonic motion 
received from an eccentric H opposite the 
crank is combined with that from another 
eccentric V at right angles to the first, the resultant motion is 
equivalent to that which would be obtained from an eccentric 
located at Eo (found by constructing the parallelogram OVEoH), 



v'e *e' 



Fig. 201. 



320 HEAT-POWER ENGINEERING 

and a valve receiving this combined motion would operate satis- 
factorily. Oil is made equal to the lap plus lead, and OV may 
be varied to change the angle of advance and throw of the equiv- 
alent eccentric £o, which has HEo as its path and resembles the 
single variable eccentric previously discussed. 

The Walschaert Valve Gear shown in Fig. 202 uses this prin- 
ciple. If the link block d is shifted to the middle e of the link, 
point c will remain practically stationary. Then the lever ab, 



Crosshead Pin ^"^--J--''' 

Fig. 202. — Walschaert Radial Gear. 

which is pivoted at c and receives motion at a from the cross- 
head, will vibrate in such manner that the end h will displace 
the valve a distance equal to lap plus lead when the crosshead 
reaches the end of its stroke, and that the valve motion will 
equal that received from eccentric 0^ in Fig. 201. The Hnk/g 
receives motion from an eccentric £, which is 90 degrees out of 
phase with the other motion. With link block in any position 
d (other than central) on the link, point c, and consequently h, 
will receive this motion, which is equivalent to that obtained 
from eccentric OV in Fig. 201. The resultant motion of the 
valve is that which would be given by the eccentric OE^. 

By shifting the link block d the amplitude of its motion can 
be varied, and this is accompanied with corresponding change 
in the width of valve opening and time of cut-off. If shifted 
above the pivot e, the engine would be reversed. 

The Walschaert gear is widely used on locomotives of the 
largest sizes. Being located on the outer side of the engine, it 
places no Hmitation on the size of the boiler, as does the Stephen- 



THE VALVE GEARS OF STEAM ENGINES 



son link gear, which is located directly below the boiler and re- 
quires considerable room for shifting from one full-gear position 
to the other. 

164. Poppet Valves and Their Gears, (a) Poppet-lift valves 
(Figs. 203 and 204) have no friction nor wear from sliding. 





Fig. 203 Fig. 204. 

They require no lubrication, and being symmetrical do not warp 
with temperature changes; hence they are suitable for use with 




Fig. 205. 
highly superheated steam. The ordinary single poppet or 
mushroom valve, Fig. 203, is hard to open because of the un- 



322 HEAT-POWER ENGINEERING 

balanced pressure on its back; therefore, the double-seated type 
of valve, one form of which is shown in Fig. 204, is commonly 
used instead, since the steam pressures on upper and lower sides 
are about equal.* 

There is a great variety of arrangements of such valves and 
of their gears. 

(b) The valve may be operated by a continuously rotating 
cam; and there may be a sleeve with variable cam surface which 
may be moved endways to change the valve events. 

(c) An oscillating cam, as a in Fig. 205, may be used, and it 
may be driven by an eccentric which is shifted by a shaft type 
of governor, as in the figure ; or it may be driven by a fixed eccen- 
tric, in which case the cut-off may be operated by trip or by 
shifting the cam, or by changing some intermediate linkage to 
distort the motion; or closure may be brought about by some 
other means. 

(d) The valve may be operated by a floating lever which ful- 
crums on a cam surface, as b in Fig. 205, and which is driven by 
an eccentric, which may be variable or stationary. The cut-off 
can be changed by any of the methods given in (c). 

(e) Cams are also used to operate other types of valves, such 
as piston valves and gridiron valves. 

* Allowance must be made for the area of the valve stem. 



CHAPTER XX. 

CONVENTIONAL INDICATOR DIAGRAM. 

165. Conventional Diagram for Simple Engines, (a) If the 

actual indicator diagram has been obtained from an engine, the 
m.e.p. may be determined by any of the methods discussed in 
Section 102, and the i.h.p. of the engine may be obtained by 
using Eq. 210. In making such computation for a double-act- 
ing engine, however, the area of the piston rod must be deducted 
from the area of the piston on one side, and the average of the 
areas on the two sides of the piston must be used in the formula ; 
or else the i.h.p. for each side of the piston must be computed 
separately. 

(b) When actual indicator diagrams are not available, it is 
customary to use a conventional diagram, with proper correc- 
tion factor, for estimating the probable m.e.p. 

(c) Before the conventional diagrams can be drawn, however, 
the clearance volume in the cylinder must be known. This vol- 
ume can be determined by pouring , 

a measured quantity of water into 
the clearance space. It can also be 
found approximately from the actual 
indicator diagram in the following 
manner (shown in Fig. 206) : Select 
two points 1 and 2 on the expansion ° F' 6 

line and draw a rectangle with these 

points as corners and with the sides parallel to the respective 
PV-axes. Then, the diagonal through the other corners will cut 
the V-axis at the origin 0, assuming that the expansion equation 
is PF = constant. Then CI in the figure is the clearance vol- 
ume to scale. The compression curve may be used in a similar 
manner to find 0. This makes application of the construction 
shown in Fig. 11. 

The clearance volumes used in practice are about as follows: 

Single-valve engine 5 to 15% 

Multi- valve engines 2 to 8% 

323 



324 



HEAT-POWER ENGINEERING 



(d) In constructing conventional diagrams for estimating the 
probable power of an engine, it is customary to assume that 
expansion follows the equation PV = PiVi = P2V2 = constant, 
instead of being adiabatic. This is because the " equilateral 
hyperbola" is easier to construct than the adiabatic curve, and 
because the actual expansion line follows it as closely as it does 
the latter. The expansion line may be constructed by the 
methods shown in Figs, ii and 12. 

The foot-pounds of work (A) represented by the area (Fig. 
207) under such an expansion line is found in the manner already 
discussed in Section 29 (c) to be 

^p,v=p.v.l/J 
V2 



PiFi log. 



Fx 



PiFiloger,* 



(276) 
(277) 



. F. 



where r is the ratio of expansion (7^]- In Fig. 208 

(e) In the case of an engine without clearance the conven- 
tional diagram is abcde of Fig. 208. The work shown by area 





Fig. 207. Fig. 208. 

Ai is PiFi foot-pounds, and that represented by A2 is PiVi 
loge r. Hence if the back pressure is P2, the work shown by 
the conventional diagram abcde is 

PlFi + PlFi loge r - P2V2 =PmV2, 

in which P™ is the mean effective pressure. Solving this equa- 
tion for Pm gives 

As the m.e.p. is generally used in pounds per square inch, it is 

* Loge = 2.302 logio. 



CONVENTIONAL INDICATOR DIAGRAM 



325 



more convenient to divide both sides of this equation by 144, 
giving 

n -I- Incr. r~\ 

P2 (278) 



P.-p{^^^ 



The values of the bracketed quantity for different values of 
r are given in Table V. 

TABLE V. 





I + log, r 




I + loge r 




i + log,r 
















^ 




r 




*" 


1.0 


1. 00 


6.0 


0.46s 


16.0 


0.236 


I 


5 





937 


7 





0.421 


17.0 


0.226 


2 








847 







0.38s 


18.0 


0.216 


2 


5 





766 


9 





0.355 


19.0 


0.208 


3 








700 


10 





0.330 


20.0 


0.200 


3 


5 





644 


II 





0.309 


21.0 


0.192 


4 








597 


12 





0.290 


22.0 


0.186 


4 


5 





556 


13 





0.274 


23.0 


0.180 


S 








522 


14 





0.260 


24.0 


0.174 


5. 5 


0.492 


15.0 


0.247 


25.0 


0.169 



(f) The actual indicator diagram of course differs from the 
computed one drawn by this method. The ratio of the area 
of the actual to that of the conventional diagram is called the 
" Diagram Factor " {DF). Then if the diagram factor is known 
for engines similar to that which is being considered, the prob- 
able m.e.p. for the new engine is 

Pm' - DFxPm (279) 

It is a common practice to use Eq. (278) even for engines 
which have clearance, and to substitute ( — r-Ti' — -7^^ ) for r, thus 



\cut-off ratio J 
ignoring the clearance. 

The diagram factors to be used for different types of engines 
in such cases are given in the following table : 

TABLE VI. — DIAGRAM FACTORS. 

Simple slide-valve engine 55 to 90% 

Simple Corliss engine 85 to 90 

Compound slide-valve engine 55 to 80 

Compound Corliss engine 75 to 85 

Triple-expansion engines 55 to 70 

(g) The conventional diagram for an engine with clearance 
is shown by ahcde in Fig. 209. Here the ratio of expansion is 

r= (L-f 4)- (/ + 4),. .... (280) 
using scalar distances to represent volumes. 



326 



HEAT-POWER ENGINEERING 



The net work shown by the area is 

A = Ai + A2- As 

= P,l-\-PUh + l)loger-P,L. 



(281) 



Dividing by L and by 144 gives the mean effective pressure for 
this case as follows: 



A \ l + (h^l)\oger l 



(282) 



To simplify this expression, let C = y- = cut-off ratio, and -f = c 



clearance ratio ; then 

Pm= pi 5C+ (C + C) \0ger\ - P2. 



(283) 



The diagram factors for this case are 3 or 4 per cent larger 
than those given in Table VI. 



'it:—^—\ 




W_l 




Fig. 209. 

(h) With compression, the diagram of Fig. 209 is reduced by 
the area D in Fig. 210. 

If pf is the pressure at the end of compression, the reduction 
of the m.e.p. caused by this small area is evidently 



from which, since 

PmD = p2 



^ (k\ ( k + lc \ p2h 

p2 (4 + Ic) 



pf = 

k + /c\ , k-\rh p2k 



L /^^^ L 



Subtracting this from Eq. 282 and letting k represent the 
compression ratio (yj, gives the m.e.p. of diagram abcdef as 

■ Pm=pl {C+(C+C) \0ger] -p2^1-k-\-(k^c) l0g«^^ I . (284) 



CONVENTIONAL INDICATOR DIAGRAM 



327 



In this case the diagram factors are 4 to 6 per cent larger 
than the values given in Table VI. 

(i) A conventional diagram that approaches closer to the 
actual diagram than any that have been discussed is shown in 
Fig. 211. This has the sloping admission line. The area is 
made up of the triangle A and the area B, similar to that for 





1 


. & 




He 






^« 




m^ 


e 


u 


li 










\ 





-i-e)r-i-k 



I I I V 



Fig. 210. 



Fig. 211. 



which Eq. 284 was developed, and much less correction is nec- 
essary for obtaining the probable m.e.p. than in the previous 
cases. 

(j) For noncondensing simple slide-valve engines operating 
under ordinary conditions, with steam pressure about 100 pounds 
gauge, the m.e.p. at the most economical cut-off is about one- 
half the initial gauge pressure. For simple Corliss engines the 
m.e.p. is about four-tenths the initial gauge pressure, under the 
same conditions. 

These values may be used only when the estimates are very 
approximate. 

166. Conventional Diagrams for Multiple-Expansion En- 
gines, (a) By referring to Fig. 93, on which diagrams of both 
the high-pressure and the low-pressure cylinders of a compound 
engine are drawn to the same scale, it will be seen that if 
the dividing line at Tr is omitted, there results a single indi- 
cator diagram of area equal to the sum of the areas H.P. and 
L.P.; thus, theoretically, a simple engine of the same size as 
the lower-pressure cylinder (total volume = V2) would give the 
same amount of power with this single diagram as is obtained 
with the two cylinders of the compound engine. 

Evidently, then, to calculate the i.h.p. of the compound en- 
gine, it is only necessary to consider the m.e.p. of this simple 



328 HEAT-POWER ENGINEERING 

(or "combined ") diagram as acting on the low-pressure piston. 
The i.h.p. of triple- and quadruple-expansion engines can be 
computed in a similar manner. 

The m.e.p. of the combined diagram is usually called the 
" m.e.p. referred to the low-pressure cylinder," or more briefly 
the " referred m.e.p." Its theoretical value can be computed 
by Eqs. (278), (283), or (284), and the probable m.e.p. is found 
by correcting with the diagram factor. Values of the latter are 
given in Table VI for use with Eq. (278). Modified values 
should be used with Eqs. (283) and (284). 

(b) If it is desired to estimate the size of a compound engine 
that will give a specified amount of power, the referred m.e.p. 
is first computed; then with the stroke, L (feet), and number n 
of cycles per minute selected, the area of the low-pressure piston 
(square inches) to give any i.h.p. can be computed from 

_ i.h.p. X 33,000 ..o . 

''''~ Pr.B^DFxLXn'' .... (285) 

in which DF is the diagram factor (see Table VI). 

Then with the ratio R of low-pressure cylinder volume to 
that of the high-pressure cylinder known, the area of the high- 
pressure piston is of course 1/R th of the low-pressure area if the 
strokes are equal. 

The size of the cylinders in triple- and quadruple-expansion 
engines is found in similar manner. The cylinder ratios to be 
used are found in Section 170. 

(c) The diagrams of multiple-expansion engines will now be 
considered more in detail, and to facilitate the discussion the 
engines will be divided into two groups: (i) the Woolf type, 
without receivers; and (2) engines with receivers. 

167. Diagrams of Woolf Type of Engine, (a) The com- 
pound engine was patented in 1781 by Jonathan Hornblower, 
but Watt's broad patents on expansion steam engines delayed 
its use. In 1804, Woolf reintroduced the compound engine and 
used an arrangement in which the steam was exhausted from 
the high-pressure cylinder, directly through very short passages 
to the low-pressure cylinder. Because there is little or no re- 
ceiver volume or storage volume between the cylinders in such 
an engine, it is necessary for the pistons to start and finish their 
strokes together, and the low-pressure cylinder must receive steam 



CONVENTIONAL INDICATOR DIAGRAM 



329 



throughout its entire stroke from the high-pressure cylinder. If the 
steam were cut off in the low-pressure cylinder, there would be 
no place into which the high-pressure steam could be exhausted 
during the remainder of the stroke after this cut-off had occurred. 
The pistons may move together or in opposite directions. 

(b) Fig. 212 (a) shows a Woolf engine whose pistons move 
synchronously and in the same direction. This motion would 
result if both piston rods were connected to the same end of a 
"walking beam" or to cranks set together. In Fig. 212 {h) 
the indicator diagram H is for 
the headend of the high-pressure 
cylinder and L is for the crank 
end of the low-pressure cylin- 
der, clearance volume being 
neglected in both cases. In 
operation, steam is admitted to 
the high-pressure cylinder ac- 
cording to line ahc; it is cut off 
at c ; is expanded along cd ; and 
it is exhausted from the high- 
pressure cylinder along line da. 
This steam exhausted from the 
high-pressure cylinder is re- 
ceived by the low-pressure 
cylinder along the line ABC Sind 

is then exhausted along line CD A. BC and da will be called 
hereafter the line of transference or receiver line. In Fig. 212 
{h) the indicator cards of both cylinders have the same length, 
that is, the abscissas are piston positions, and are numbered to 
correspond with the positions shown in Fig. 212 (a). 

In Fig. 212 (c) the diagrams have been " combined," with 
abscissas representing the respective volumes in the two cyl- 
inders. In Fig. 212 {d) the diagrams have been combined in 
such a way that the volume of the steam during transference 
from the first to the second cylinder can be scaled directly. 
Thus, when the pistons have reached simultaneous positions 2 
and 2' the distance 0^-2' (= ox) is the volume of steam in the 
high-pressure cylinder, the distance 4-2 ( = oX) is the volume it 
occupies in the low-pressure cylinder, and distance 2^-2 ( = Xx) 
is the total volume of the steam between the two pistons for 




b\ ^ 

H ^^d 



Fig. 212. 



330 EEAT-POWER ENGINEERING 

this position in the stroke. Obviously, the distances between 
piston positions bearing like numbers in this figure represent 
the volumes of steam during the period of transference. After 
these volumes have been determined (by scaling), the pressures 
at the corresponding piston positions can be found if the expan- 
sion is assumed to be hyperbolic, for during expansions cd, da, 
and BC the product PV remains constant, since there is no 
change in the quantity of steam involved during these processes. 
Thus the high- and low-pressure PV-diagrams can be readily 
constructed. 

i68. Diagrams for Engines with Infinite Receivers and No 
Clearance (General), (a) If a receiver of infinite volume is 
placed between the cylinders of the Woolf engine the curves da 
and BC, in Fig. 212, would become horizontal straight lines, and 
the low-pressure indicator diagram would be a rectangle. Evi- 
dently, with finite receiver, the larger the receiver volume the 
more nearly horizontal and straight will the line of transference 
become. 

With a receiver of considerable volume into which the high- 
pressure cylinder can exhaust, it is possible to " cut off " in 
the low-pressure cylinder and thus to expand the steam inde- 
pendently in this cylinder. The pressure of the receiver will 
vary, because part of the time steam is being received from the 
high-pressure cylinder, at other times steam is being delivered 
to the low-pressure cylinder, and during part of the cycle both 
of these operations may occur simultaneously. Consequently 
the back-pressure line on the H.P. indicator diagram and the 
admission line of the L.P. diagram will be irregular. The 
character of the line of transference will be discussed in detail 
later. 

(b) When a receiver of considerable volume is used it is pos- 
sible to have any angle between the 
cranks of the two cylinders, whereas in 
the Woolf engine this angle is limited to 
zero degrees or 1 80 degrees in cases where 
there is a separate crank for each cylinder. 
(c) In Fig. 213, AhcD is a conventional 
Fig. 213. " combined " diagram for a compound 

engine with receiver of infinite volume. In it, AD \s the volume 



CONVENTIONAL INDICATOR DIAGRAM 331 

of the low-pressure cylinder, ad is that of the high-pressure cyl- 
inder, he is the volume of steam admitted to the high-pressure 
cylinder, and BC \s that at the time of cut-off in the low-pressure 
cylinder. Then 

-r- =fH = ratio of expansion in the high-pressure cylinder ; 

AD . , . . , , 

^7; = rL= ratio or expansion in the low-pressure cylinder ; 

AD , • r 

-T-- = rT= total ratio 01 expansion. 

Since, if hyperbolic expansion is assumed, 
pc{bc) = Pd{ad), 
the receiver pressure is evidently 

'he' 



h-h 



(286) 



for the case in which the expansion is complete in both cylinders. 

(d) It is evident that the horizontal transfer line obtained 
with a receiver of infinite volume would correspond to the mean 
transfer pressure if a receiver of finite volume is used, and that 
indicator diagrams drawn with this horizontal transfer line would 
have practically the same areas as with the variable line of the 
small receiver. Hence these diagrams may not only be used 
for the engine as a whole but also when each cylinder is con- 
sidered separately. 

(e) Changing the low-pressure cut-off to make it occur earlier 
results (i) in raising the receiver line, as shown dotted in Fig. 213; 
it also results (2) in a reduction of the area of the high-pressure 
diagram and (3) an increase in the area of the low-pressure dia- 
gram. Making the low-pressure cut-off later reverses these re- 
sults. Thus the cut-off in the low-pressure cylinder influences the 
receiver pressure and distribution of work between the cylinders, 
but does not affect the total work done by the engine. 

(f) The selection of the receiver pressure is based on the fol- 
lowing considerations: 

(i) For greatest economy in the use of steam the temperature 
ranges in the two cylinders should probably be equal, although 
this is not certain. Hence the receiver pressure should probably 
be such that the corresponding temperature of the steam is 



332 HEAT-POWER ENGINEERING 

midway between the initial and final temperatures of the work- 
ing fluid. Other considerations may be more important than 
this, however. 

(2) It is sometimes desirable to have the same cut-off (that is, 
the same expansion ratios) in both cylinders. For example, 
in the tandem compound engine shown in Fig. 107, the two 
valves are on the same rod, hence the cut-offs in the two cylin- 
ders must change together. 

(3) Usually it is desirable to have equal work done in the two 
cylinders. In this case the receiver line should be so drawn 
that the areas of the high-pressure and low-pressure diagrams 
are equal. This is especially desirable when the engine is a 
cross compound. 

(4) In some special cases, equal maximum thrusts on the 
piston rods are desirable, and these thrusts are dependent on the 
receiver pressure. 

(5) The uniformity of turning effort is dependent on the shape 
and relative proportions of the indicator diagrams of the two 
cylinders, and hence is dependent on the receiver pressure. 

Usually compound engines are operated to perform equal work 
in the two cylinders, and this gives about as uniform a crank effort 
as is possible, and hence, considerations (3) and (5) are satisfied 
together with sufffcient accuracy for ordinary purposes. 

169. Receiver Pressures in Compound Engines with Infinite 
Receivers and No Clearance, (a) It has just been seen that 
the distribution of work among the cylinders depends on the 
receiver pressures, hence the problem is one of determining the 
mean receiver pressures which will give the desired distribution. 
The receiver pressure may be determined either graphically or 
analytically, using the conventional diagram. The receiver vol- 
ume will be considered infinite and the clearance zero. 

(b) The graphical method will be considered first. 

Let pi,p2, and V2 in Fig. 214 be given, and assume a terminal 
pressure pD such as will give the drop {DE) in pressure in ac- 
cordance with Section iii. With this data available, the com- 
bined PV -diagram, AhcDE, can be easily drawn and its work 
area can be determined. If the high-pressure cylinder is to do 
1/wth of the total work, the area H will be l/nih of the total 
area. The problem then is to find the location of line ad which 



CONVENTIONAL INDICATOR DIAGRAM 



333 



will give this distribution of work. The line ad can be drawn 
tentatively and then the area above it can be integrated by 
planimeter to see if it has the proper value. If it is not correct, 
another position of ad can be tested, and by repeated trials a 
proper receiver line can be obtained by this " cut and try " 
method. This same method can be used when the H.P. expan- 
sion is incomplete (i.e., when the toe of the H.P. diagram is 
removed) as in Fig. 215, and can also be applied to multiple- 
expansion engines with any number of expansion cylinders. 



^ 




" \ 




a \d 




3 cl"^^^ 




L 
A 




' Vj: 


— JvJ" 




Fig. 214. 

In Figs. 214 and 215, Vh is the volume of the high-pressure 
cylinder; and the corresponding mean effective pressure acting 
in the high-pressure cylinder is 



pmH = 1 , T^ X scale of ordinates. 

length Vh 

Similarly the L.P. mean effective pressure is 

area L 



(287) 



PmL 



X scale of ordinates. 



length Vl 

The total m.e.p. " referred " to the low-pressure cylinder is 
area {H + L) 



pmR 



X scale of ordinates. 



(288) 



(289) 



length Vl 

(c) By removing the toe from the H.P. diagram, as in Fig. 
215, the high-pressure cylinder is decreased in volume in the 

ratio -:^-p^ and the cost of the engine is consequently reduced. 

On account of this saving, and because the expansion should not 
be to a pressure lower than that which is sufficient to overcome 
the engine friction, most compound engines are operated with 
the drop de at release in the high-pressure cylinder. 



334 HEAT-POWER ENGINEERING 

Hence, only that case will be considered in the analytical 
method which follows: 

It will be assumed that the expansion is hyperbolic, that the 
receiver volume is infinite, and that the clearance volumes are 
zero. 

(d) In Fig. 215, let 
pi = Initial pressure (lbs. sq. in.) ; 
p2 = L.P. back pressure (lbs. sq. in.) ; 
pR= Receiver pressure (lbs. sq. in.); 
pD = Release pressure in low-pressure cylinder ; 
R = Cylinder ratio = (vol. low-pressure cylinder) -i- (vol. 
high-pressure cylinder) = Vl/Vh 
= (area low-pressure piston) -^ (area high-pressure piston) 
when the piston strokes are equal, as they usually are. 

r^ = Total ratio of expansion = t^ = -^f^ ; 

Pd 1^1 

Vh 
Tji = Ratio of expansion in high-pressure cylinder = ^^ ; 

Vi 

Vl 
rj, = Ratio of expansion in the low-pressure cylinder = :^ ; 

Vc 

pmH = M.e.p. of the steam in high-pressure cylinder (pounds 

square inch) ; 
pmL = M.e.p. of the steam in low-pressure cylinder (pounds 

square inch) ; 
i>mB = Total m.e.p. "referred" to the low-pressure cylinder 
(pounds square inch). 

Since 

r -^ 



and since 



i = Yii^YH^iyL\^ IVl\ 
1 ViVl \yj • \Vh) 

Vl , Fl „ 

■TT = i't and 77- = R, 
Vl Vh 



it is evident that the ratio of expansion in the highrpressure 
cylinder is 

rjj = rT-^ R (290) 

(e) As the L.P. piston is R times as large as the H.P. piston 
(the strokes being assumed equal), the intensity of pressure on 
the L.P. piston that would do work equal that due to the H.P. 
mean effective pressure is evidently pmn/ R- Then if the high- 



CONVENTIONAL INDICATOR DIAGRAM 



335 



pressure cylinder is to do 1/n th of the total work, it must follow 
that the H.P. m.e.p. referred to the L.P. piston will be equal to 

^ , hence 

n 

Now, from Eq. (278), 
and 



PmH ^ pmR 

R n 



PmH = Pi — :;: - pR, 



PmR 



n + loge rj\ 



P2\^XK, 



(291) 
(292) 
(293) 



in which i^ is a factor introduced to correct for the loss due to 
the omission of the toe of the H.P.-diagram. It ranges from 
0.9 to i.o, the latter value being for the complete expansion in 
the high-pressure cylinder. 

Substituting for p^H and pmR in Eq, (291) and solving for pj^, 
results in the following expression for the receiver pressure which 
will give the desired distribution of work: 

loge rH\ KR Wl + loge rn 



pR 



[(^ 



rr 



'"j-m- 



(294) 



(f) With pR known the ratio of expansion in the low-pressure 
cylinder can then be found. 
Pi 



Since .^=^ = g(seeFig. 215) 



and since po 



it follows that 



rL = 



rj,. 



(295) 



(g) This analytical method not only applies 2\ 
to two-stage compound engines but also to 
multiple-expansion engines having any 
number of expansion cylinders. Thus, if "' 
the work is equally distributed among x P„„ 
cylinders (for example, x = 3 in Fig. 216), p 
the work in the first cylinder is 1/x th of 
the total. Then the pressure {pn^ in the first 
receiver can be found from Eq. (294), with x substituted for n. 

The second cylinder receives steam at this same receiver pres- 



Fig. 216. 



336 HEAT-POWER ENGINEERING 

sure (pRi) ; and this cylinder and the succeeding ones can be 

considered as constituting another engine with initial pressure 

equal to pR^ and with (x — 1) cylinders. This engine will do 

(x — 1) 

parts of the work of the whole engine, and this second 

X 

cylinder (considered now as a high-pressure cylinder) will do 

7 -rth of this work. Then the pressure (pR,) in the second 

{x - 1) 

receiver can be found by again using Eq. (294) with (x — 1) sub- 
stituted for n and by making such other changes as will be 
apparent. Pressures in succeeding receivers (if any) can be 
found in like manner. 

(h) In a triple-expansion engine, after the ratio R of low- 
pressure cylinder to high-pressure and ratio Rm of LP. to H.P. 
have been selected, it is evident (since Vl— F^yi? and Vi=VhRih) 
that the cylinder ratio Rli of L.P. to I. P. is 

(i) Following (f) of this section, the ratio of expansion in the 
low-pressure cylhider is 

'•^=(f')'T (^97) 

Also, by analogy, r^ = [~r^ ) ^r , in which rj' is the total expansion 

\PrJ 
in the intermediate-pressure and the low-pressure cylinders com- 
bined. After rL is known, r^^^ can be computed from rrj,^= rj^ ( — M- 

Then by comparison with Eq. (290) it is seen that the ratio 
of expansion in the intermediate- pressure cylinder is 

^'='-"^-=^(£) (^^«> 

The ratios of expansion in a quadruple-expansion engine would 
be determined in a similar manner. 

170. Cylinder and Expansion Ratios Used in Multiple-Ex- 
pansion Engines, (a) In general the greater the total range of 
pressures in the engine the larger should be the cylinder ratio 
and the expansion ratio. Thus high-pressure engines have 



CONVENTIONAL INDICATOR DIAGRAM 337 

larger ratios than low-pressure engines, and those condensing 
have greater ratios than those which operate noncondensing. 
Practice varies widely and only the average values can be 
given here. 

(b) Modern compound engines usually operate with steam 
pressures between 125 pounds and 150 pounds gauge. In many 
instances, however, much higher and lower values have been 
used. Stationary engines of this type usually have cut-offs in 
the high-pressure cylinders between 0.25 and 0.4 of the stroke 
under normal load. With late cut-off a smaller engine can be 
used for a given power than with early cut-off; but the conse- 
quent saving in " first cost " of engine may be more than 
balanced by loss in efficiency and greater cost of operation. 
Cylinder ratios customarily used are about as follows: 

CYLINDER RATIOS FOR COMPOUND ENGINES. 

Cylinder ratio 2| 2>\ 4 41 

Gauge pressiire, noncondensing 100 120 

Gauge pressure, condensing 100 120 150 

Dividing the cylinder ratio by the H.P. cut-off fraction (0.25 
to 0.4) gives the total ratio of expansion. What the best cyl- 
inder and expansion ratios are, is still under discussion. Some 
advocate cylinder ratios even as large as 6 or 7 and remarkable 
economies have been obtained with such.* 

(c) The ratio of expansion is sometimes fixed by first assum- 
ing the pressure drop at release. If this drop is added to the 
L.P. exhaust pressure, the pressure {pri in Fig. 215) at release 
is obtained. Then, considering the expansion to be hyperbolic, 
the total ratio of expansion on the conventional diagram is 

^T= jr^ (^99) 

Pd 
which is approximated more or less closely in the actual case. 
If the expansion ratio (rn) in the high-pressure cylinder is then 
selected, the cylinder ratio is 

i?=^ (300) 

*r =6.25 Cross Compound Corliss. Am. Electrician, June, 1903. 
tt =7-3 Fleming Four-valve. Trans. A. S. M. E., Vol. XXV, page 212. 
rr = 6 .4 Tandem Compound Corliss — Barrus' Engine Tests, page 185. 
fT = 6.2 Edison Waterside Station, New York. Power, July, 1904, page 424. 
Also see papers in Trans. A. S. M. E. 



338 HEAT-POWER ENGINEERING 

After the receiver pressure, which will give the proper distri- 
bution of work between the cylinders, has been determined, the 
drop in pressure at H.P. release should be checked. 

(d) Modern triple-expansion engines usually operate with 
steam pressures from 150 pounds to 180 pounds gauge or even 
higher. The pressure at L.P. release in condensing marine en- 
gines is commonly about 15 pounds per square inch absolute under 
normal load, and in stationary engines it is about half this value. 
As before, the total expansion ratio (r^) can be found approx- 
imately by dividing the initial pressure by the L.P. release pres- 
sure (considering the expansion to be hyperbolic) ; or it can be 
obtained from economy curves of similar engines operating under 
similar conditions, when ratios have been used as abscissas. 

The H.P. cut-off in marine engines is usually from 0.55 to 0.7 
of the stroke and in stationary engines is much earlier. The 
H.P. expansion ratio {rn) is the reciprocal of this cut-off ratio 
(neglecting clearance). With r^ and th known, the volume 

ratio of high-pressure to low-pressure cylinder is i? = — . If 

the strokes are equal, as is almost invariably the case, the ratio 
of piston areas will be the same as the volume ratio. 

If the conventional diagrams of the various cylinders have 
sharp toes, the work will be equally distributed among the cylin- 
ders if the cylinder volumes (or piston areas) are such that 

TT T 

-y = Y (i^ which the letters refer to the high-, intermediate, 

and low-pressure cylinder volumes, or areas). In such a case the 
intermediate cylinder volume (or piston area) is found from 

/= Vhx L. 
In the actual case, because of departure of the real indicator 
diagrams from the theoretical and because of cylinder conden- 
sation, cushion steam, etc., the intermediate-pressure cylinder is 
made a little smaller than this equation would give. Seaton* 
states that in marine practice the intermediate cylinder volume 
(or piston area) is about as given by the following equation : 

, Vhx L 



1.1 



(301) 



* Seaton's "Manual of Marine Engineering"; or Seaton and Rounthwaite's 
'Pocket Book of Marine Engineering." 



CONVENTIONAL INDICATOR DIAGRAM 339 

Marine triple-expansion engines are proportioned about as 
follows : 



Initial pressure, abs. . . 

Ratio/ to H 

Ratio LtoH 

Total expansion ratio. 



165 


175 


19s 


2-33 


2.4 


2.54 


6.6 


7.0 


7.8 


I. 


II. 7 


13- 



(e) Quadruple-expansion engines usually operate with pressures 
from 175 to 225 pounds gauge. The L.P. terminal pressures 
and H.P. cut-off percentages are about the same as for triple- 
expansion engines. Thus the total expansion ratios are some- 
what larger than in the latter engines. If the ratios of adjacent 
cylinders are made equal, then 

H h h " 

in which Ix and /2 refer to the first and second intermediate 
cylinders. From which it follows that 

h = R.H ........ . (302) 

h = RJi = R.'H (303) 

L = RJ2 = Rm (304) 

Hence the ratio of adjacent cylinders (assuming-^ known) is 

Ii 



V 77' 



^ (305) 

or the ratio of low-pressure to high-pressure cylinder (assuming 
Rx known) is 

R = ^=R.\ . (306) 

After Rx, H, and L are known, /i and I2 follow from Eqs. 
(302), (303). These values of /i and I2 should be reduced some- 
what, for the same reasons that were given in the case of the 
triple-expansion engine. 

In quadruple-expansion marine engines the cylinders are about 
in the following proportions: — i : 1.8 : 3.6 : 7.8. A study* of 
14 different quadruple-expansion engines, with pressures about 

* H. H. Suplee. Trans. A. S. M. E., Vol. X, page 583. 



340 HEAT-POWER ENGINEERING 

1 80 pounds per square inch, showed the average cylinder propor- 
tions to be 1 : 2 : 3.78 : 7.70; or nearly 1:2:4:8.* 

171. The Theoretical Indicator Diagram of Multiple-Expan- 
sion Engines with Clearance. In the foregoing discussion 
clearance was neglected. If clearance is 
'^ " considered, the results will be changed 

somewhat. In such cases the analytical 
method is a little complicated, hence the 



-— Zx — 'i^^ graphical method is generally the best one 
r '^L 1 to use. This method needs no explanation. 



Fig. 217. 



In the theoretical cards of a compound 
engine with clearance, as shown in Fig. 217, 
the total ratio of expansion is 

_ Ll+CIl 
""- Ih+CIh' 
the H.P. ratio of expansion is 

Lh + CIh 



rn 



the cylinder ratio is 



Ih + CIh 






and the H.P. and L.P. cut-off ratios are respectively^ and -7^- 

J-'H -Ll 

172. Effects of Changing the Cut-offs in the Respective 
Cylinders of Multiple-Expansion Engines, (a) In " regulating " 
the engine to make the power output equal to the demand, the 
steam distribution to the cylinders can be varied in several ways. 

(b) It has already been shown that the effect of making the 
L.P. cut-off occur later in the stroke (other things remaining the 
same) is (i) to lower the receiver pressure, (2) to increase the 
H.P. work, (3) to decrease the L.P. work; and vice versa. But 
(4) such change does not affect the total work of the engine if 
the toes of the diagrams are not lost, hence the engine cannot 
be regulated by changing merely the L.P. cut-off. 

(c) If the L.P. cut-off is fixed, and the H.P. cut-off is made to 

* For data relating to multiple-expansion marine engines, see Seaton's " Manual 
of Marine Engineering," Robertson's "Translation of Bauer's Marine Engines and 
Boilers." For all types of multiple-expansion engines, see Heck's "The Steam 
Engine," Vol. II, pages 506-9, and Gebhardt's "Steam Power Plant Engineering." 



CONVENTIONAL INDICATOR DIAGRAM 



341 



occur later, there results (i) an increase in the receiver pressure 
(Fig. 218), (2) a greater increase in the L. P. work than in 
the H.P. work. Making H.P. cut-off occur 
earlier produces the reverse effects. Com- 
pound engines can be regulated by having an 
automatic governor control only the cut-off 
in the high-pressure cylinder. But in such 
case, if there is much change in the load on 
the engine, the L.P. cut-off should be ad- 
justed by hand to equalize the distribution 
of the load between the cylinders. 

(d) If the initial, receiver, and exhaust pressure lines on a 
PV-diagram for a compound engine are extended from one hy- 
perbolic expansion line to another, as from cD to c'D' in Fig. 219 
(a), it will be found (i) that the expansion ratios in the cylinders 




Fig. 218. 



a cK 


(«) 


B c\ 

A 








Fig. 219. 



remain unchanged; and that, in consequence, (2) the propor- 
tionate distribution of work between the cylinders also remains 
the same. 

In Fig. 219 {b) it is seen that the high and low cylinder volumes 
{Vh and Vl) are such that the expansion lines cd and CD in 
the two cylinders are complete and continuous. If the cylinder 
volumes are related thus, and if the cut-offs are advanced pro- 
portionately (so that c'd' and C' D' in Fig. 219 {b) are on the same 
hyperbola), the distribution of work can be shown to be in the 
same proportion as in the case of complete expansion just dis- 
cussed; and further (from this), that (3) the toe areas {Xh and 
Xl) lost will be in this same proportion. These same state- 
ments are also true in case the cut-offs are decreased propor- 
tionately as in Fig. 220. In this figure, however, it is seen that 
the diagrams have " loops " Xh and Xl, which represent nega- 



342 



HEAT-POWER ENGINEERING 




Fig. 220. 



tive work. Evidently the cut-off should not be earHer than c^ 
if good economy is important. 

With such arrangement the automatic governor can be made 
to change the cut-off equally in the two cylinders and the proper 
balance of work will be always auto- 
matically maintained. The tandem com- 
pound engine in Fig. 107 is an example 
of this case. 

If the L.P. toe loss is greater than the 
similar H.P. loss, it can be shown that 
to maintain the same relative balance of 
power between the cylinders, the L.P. 
cut-off must vary more rapidly than the 
H.P. cut-off; thus as the power is in- 
creased the receiver pressure must be raised. 

(e) If the cut-offs (or expansion ratios) in the two cylinders 
remain constant, the power of the engine may be decreased 
by throttling the steam, and in this case the distribution of 
power between the cylinders remains in substantially the 
same proportion. That this is true may be seen from inspec- 
tion of Eq. (294), in which pR is seen to be practically propor- 
tional to pi (since all other quantities are constants in this 
case, except the ratio P2/P1, which is so small a quantity that 
its change is negligible). This shows that the effect of throt- 
tling is substantially equivalent to changing the pressure scale 
of the diagram. 

(f) Because of the effect of clearance, " wire drawing," cyl- 
inder condensation, etc., the real 
diagrams differ greatly from the 
theoretical ones, hence the conclu- 
sions just given can be used only 
in a very general sense in actual 
cases. 

173. Theoretical PV-Diagrams 
of a Tandem Compound Engine 
with Receiver of Finite Volume, 
and having Clearance, (a) Fig. 
221 shows the PV-diagrams for a tandem compound engine 
which has clearance volume and finite receiver volume. The 




Fig. 221. 



CONVENTIONAL INDICATOR DIAGRAM 343 

abscissas of both the H.P. and L.P. diagrams are the strokes 
(same for both cyHnders). OF is the hne of absolute zero for 
volumes in the low-pressure cylinder, and oy is the similar line 
for the high-pressure cylinder. In the latter cylinder ahc is 
the admission line, cd is the expansion line (with respect to axes 
oy and oO), ddi is the drop in pressure when the H.P. steam 
is released to the receiver, diei is the period when the high-pres- 
sure cyhnder is exhausting into the receiver alone, and def is 
the period during which the high-pressure cylinder is exhausting 
into both the receiver and the low-pressure cylinder; fg shows 
the period when the high-pressure cylinder is exhausting into 
the receiver, after cut-off has taken place (at C) in the low-pressure 
cylinder; and ga is the compression into the H.P. clearance 
space (and is therefore asymptotic to oy). Evidently if O'Y' is 
drawn to the right of oy at a distance {Vr) equal to the receiver 
volume (measured to the same scale that is used for the H.P. 
volumes) , fg will be a hyperbola with axes 0' Y' and O'O. Dur- 
ing the period ef of the H.P. exhaust the low-pressure cylinder 
is receiving steam along the coincident line BC. After L.P. 
cut-off at C, the steam in the low-pressure cylinder expands 
according to CD, is exhausted along DEF, compressed along 
FA, and admitted along ABC from the high-pressure cylinder 
and from the receiver. Evidently CD and FA are hyperbolas 
with respect to axes Oo and OY. 

(b) These diagrams can also be constructed by the method 
given in the next section. 

174. Theoretical PV-Diagrams of a Cross Compound Engine 
with Receiver of Finite Volume, and having Clearance, (a) In 

Fig. 222 (a) the H.P. and L.P. diagrams of opposite strokes are 
shown with true volumes as abscissas, and with the clearance 
and receiver volumes in proper proportion and relation for a 
single-acting cross compound engine with L.P. cut-off less than 
one-half stroke. It will be seen that the arrangement of dia- 
grams is similar to that in Fig. 212 {d), but with clearance and 
receiver volumes added. 

If the points in the stroke at which the valve events occur are 
known, the lines abed and EFA are easily drawn, but the points 
on the H.P. exhaust line and L.P. admission line are harder to 
find. The method of determining these will now be considered. 



344 



HEAT-POWER ENGINEERING 



(b) It will be convenient to have an auxiliary diagram, such 
as Fig. 222 (b), called a steam- distribution chart, which will 




Fig. 222. 



show for each crank angle (ordinate) the volumes (abscissas) of 
steam in both the cylinders and in the receiver. If the motion 
of the piston is harmonic (as it is approximately) , the curves of 



CONVENTIONAL INDICATOR DIAGRAM 345 

volumes displaced by the pistons are of course sinusoids, and 
can be easily constructed in the manner shown in the lower 
part of the figure. In the case under consideration, as the 
cranks are at right angles these sinusoids must differ in phase by 
90°. The clearance lines {oy' and OY') are added to the chart; 
thus the distance from a point on a sinusoid to the clearance 
line gives the volume of steam in the cylinder for the corre- 
sponding crank angle. 

The percentages of stroke for all " valve events " are sup- 
posed to be known, thus the abscissas of all events can be laid 
off on the PV-diagrams in Fig. 222 (a). Lines ahcd and EFA 
can be drawn at once, and efgha and BBxC can be drawn ten- 
tatively to show roughly the general shape of the diagrams. 
The exact lines will be found later. Then on the sinusoids, in 
Fig. 222 (&), the points for the valve events can be found by 
projecting downward from the PV-diagrams, or may be located 
more accurately by using the crank angles corresponding to the 
valve events. The points thus found are lettered the same as 
the corresponding points on the PV-diagrams, but are primed. 

(c) From h' to c' in Fig. 222 (&) is H.P. admission, and from 
c' to d' is H.P. expansion, with volumes varying according to 
the heavy abscissas to the right of the sinusoid between these 
points. The product PV is constant during this expansion 
(and its value can be found since Pc and Vc are known), hence 
the " PV-quantity " {PV)c may be taken as representing the 
whole process of expansion. Evidently the following broad 
statement can be made: 

General Proposition A: Between naive events (not neces- 
sarily in the same cylinders) controlling the weight of steam 
involved, the " PV-quantity " is constant; and when its value is 
known the expansion curve can be constructed. Thus, in this 
instance, dividing the PV-quantity (PV)c by different values 
of V gives the pressures to be used in plotting the expansion 
curves cd. 

(d) At d (and d') the steam with PV-quantity equal to {PV)c 
is released from the high-pressure cylinder and mixes with the 
receiver steam which has a PV-value equal to mn{PV)g, in 
which m and n are unknown coefficients, the value of which will 
be determined later. In such cases the following assumption is 
made: 



346 HEAT-POWER ENGINEERING 

General Proposition B: The PV -quantity resulting from a 

mixture is 

[PV]. = ^{PV) . (307) 

Thus, after point e is passed 

[PVl = {PV). + mn [PVl, . . . (308) 

from which [PV]e can be found when mn [PV]g has been deter- 
mined, since (PV)c is already known. 

(e) The L.P, compression occurs from i^ to ^ (and F' to A') 
with PV-quantity constant and equal to {PV)p, — ^ the value of 
which can be easily found, since Pp and Vp, are given, — and 
with volumes varying as shown by the heavy dotted abscissas 
to the left of sinusoidal arc i^'^'. At A (and at A' and /) 
this L.P. cushion steam mixes with that in the receiver and high- 
pressure cylinder; hence the PV- value of the mixture is, from 
Proposition B, 

[PV], = [PV]e + (PV)f (309) 

Thus during phase gh and BBi the pressures may be found by 
dividing [PF]g by the volumes which are shown by the dotted 
abscissas between arcs g'h' and A'Bi. 

(f) After the H.P. exhaust valve has closed at h there remain 
in the receiver and low-pressure cylinder n parts of the steam that 
has been represented by [PF]^, and the rest, (i — n) parts, is 
used for compression in the high-pressure cylinder. Between Bi 
and C (and Bi and C') the PV-quantity of the steam in the 
low-pressure cylinder and receiver is n [PV]g in accordance with 
the following assumption : 

General Proposition C: If a weight of steam, having a cer- 
tain PV-quantity, is divided without change in presstire, the PV- 
quantity of the part is the same fraction of the original PV-quantity 
that its weight is of the original weight. For example, if one-half 
the steam involved is left in the cylinder and receiver, when the 
H.P. exhaust closure occurs at h or Bi {h' or J5/), then n = ^, and 
the PV-quantity of this remaining steam has the value | [-PF]^. 
Thus, between points Bi and C the PV- value is w [PV\g and the 
volumes are shown by the abscissas to the left of the sinusoidal 
arc between points 5/ and C' . 

After the L.P. valve has cut off at C (and C) there are left 
in the receiver m parts of the steam which was represented by 
n [PV]g; hence, this receiver steam has a PV-value of mn [PV\g, 



CONVENTIONAL INDICATOR DIAGRAM 



347 



which continues constant until point a in the next cycle is 
reached. 

(g) In the simultaneous equations (308) and (309) all quan- 
tities are either known or can be determinable directly, except 
the bracketed quantities [PV]e and [PFj^; but these latter can be 
found by elimination. When these are known, the PV-diagrams 
can easily be completed. 

(h) If the engine is double-acting, and if it has equal PV-dia- 
grams at both ends of the cylinders, the solution of only one end is 
necessary. But if the diagrams are not equal, it is necessary to 
draw the steam-distribution chart for both ends of the cylinders. 
Then there will be four unknown PV-quantities, but there will 
be the following four simultaneous equations, from which the 
unknowns can be determined: 

[PVl= {PV).+m'n'[PV]\ . . . (310) 
[PV], = [PVl + {PV)f .... (311) 
[PF]'e = {PV)\ + mn [PV]„ . . . (312) 
[PVr, = [PVYe + (PVyF .... (313) 

in which the primed quantities are those for the cylinder ends 
not considered in the previous discussion. 




Fig. 223.- — Effect of Early Release 



(i) In the foregoing it has been assumed that release and 
admission occur at the ends of the stroke. If the engine is 
double-acting and if the steam is released before the end of the 
stroke in the high-pressure cylinder, the L.P. admission line will 
suddenly rise, in case the L.P. cut-off has not already occurred; 
for this release suddenly increases the steam pressure in the re- 
ceiver from which steam is still being supplied to one end of the 
low-pressure cylinder. This is shown in Fig. 223, from which it 



348 



HEAT-POWER ENGINEERING 



is seen that, when the steam is released at di, there is a drOp of 
pressure in the high-pressure cyhnder accompanied by a simul- 
taneous rise at X in the low-pressure cylinder, until the pres- 
sures at X' and d\ are equal. This case can be analyzed by 
the method already given. 

(j) The case with cut-off later than half-stroke is somewhat 
similar to that discussed in (i) of this section and is illustrated 
in Fig. 224. Even if the H.P. release occurs at the end of the 
stroke (at di), there will be the sudden rise XX' on the L.P. 
admission line, as the low-pressure cylinder has not previously 




Fig. 224. — Low-pressure Cut-off later than Half-stroke. 

been cut off from the receiver. From X' to cut-off at C the low- 
pressure cylinder continues to receive steam from the receiver, 
while simultaneously the high-pressure cylinder is discharging 
steam into the receiver according to line eiCi. Evidently the 
pressures at points ei and X' are equal; and the same is true of 
points ei and C. This case can be analyzed with the aid of a 
steam-distribution chart, in the same manner as that which has 
just been discussed in connection with the other cases. 



175. Theoretical PV-Diagrams of Multiple-Expansion En- 
gines with Finite Receiver and Clearance Volumes, with Any 
Number of Cylinders and with Any Angles between Cranks 
(General Case). The methods just discussed in connection with 
the construction of PV-diagrams for compound engines can be 
extended to this perfectly general case. It is assumed that the 
initial and exhaust pressures are known, together with the vol- 
ume ratios of cylinders, receivers, and clearances, and that the 



CONVENTIONAL INDICATOR DIAGRAM 



349 



percentages of stroke (or crank angles) of the various valve 
events are given. The procedure is as follows: 

(i) Draw the cylinder, clearance, and receiver volumes in proper 
relative positions on the PV-diagrams. 

(2) Sketch as much of the H.P. and L.P. PV-diagrams as 
can be done initially. 

(3) Draw the sinusoids on the steam-distribution chart in a 
proper phase relation (considering the crank angles and " se- 
quence " of cranks); locate the valve events; and by a system 
of section lining show the volumes connected between events 
(remembering that these volumes are not necessarily confined 
to those in one cylinder). 

(4) On the distribution chart: — (a) give the PV-quantities 
initially known, such as {PV)c and {PV)f in the previous cases; 
{h) in accordance with General Proposition C state the PV- 
quantities resulting from a separation of volumes (when not 
accompanied by change in pressure) as fractional parts of the 
quantity which is divided, as mn {PV)g\ and (c) in accordance 
with General Proposition B, write equations for the PV-quan- 
tities resulting from mixtures. 

(5) Obtain the values of the fractional coefficients, m, n, etc. 

(6) Find the unknown PV-quantities by solving the simul- 
taneous equations, of which there should be the same number as 
there are unknowns. 

(7) Complete the construction of the PV-diagram, which can 
be done now that the PV-quantities are all known. 

The heavy lines in Fig. 225 
show the PV-diagrams for 
triple-expansion engine. The in- 
dividual diagrams were first ob- 
tained in the manner just outlined 
and then were combined with 
respect to a common axis of 
volumes as shown in this figure. 




176. The Actual Combined In- 
dicator Diagrams of Multiple- 
Expansion Engines, (a) In Fig. 
225 it is seen that the theoretical 
PV-diagrams (in heavy lines) overlap, that their expansion 



Fig. 225. 



350 



HEAT-POWER ENGINEERING 



lines do not fall on the same hyperbola, and that the sum 
of their areas is much less than that of the simple diagram 
abcde. The overlapping parts of the diagrams do not occur 
simultaneously. The lack of continuity of the expansion lines 
is largely due to the difference in the amounts of cushion steam 
in the various cylinders; it is also due to the sloping and irregu- 
larity of the LP. and L.P. admission lines, and to earliness of 
the LP. and L.P. cut-offs compared with that in the high- 
pressure cylinder. The ratio of the sum of areas H, I, and L 
to area abcde is the theoretical diagram factor in this case, and 
it is evidently much less than unity. 

(b) The actual indicator diagrams depart considerably from 
the theoretical. This is partly because of wire drawing during 
flow of steam through valves, receivers, and piping, partly be- 
cause of condensation or reevaporation in cylinders, receiver, 
and piping, partly from radiation and similar losses, partly be- 
cause the real expansion line is not hyperbolic, and may also be 
partly due to the withdrawal of the condensate collecting in 
" separating " receivers. In Fig. 225 the probable diagrams are 
shown dotted. 

(c) Given the actual indicator cards obtained from the en- 




CK 




1 ^^^^^ 




^ 








Atmos.i 1 


.s, 




^ i 



^ 1 



Fig. 226. 

gine, as h and I in Fig. 226, they can be readily " combined," 
as shown by iJ and L, if the cylinder and clearance volumes are 
known. 



CONVENTIONAL INDICATOR DIAGRAM 35 1 

The areas of diagrams H and L can then be found and the 
" referred m.e.p." determined in the usual manner. 

After this, the actual diagram factor can be obtained by 
getting the ratio of these quantities to the area of the conven- 
tional diagram.* 

(d) On Fig. 226 the saturation curves, 6'6' and S'S', have 
been drawn. As the weights of cushion steam in the two cyl- 
inders are not the same, and because the condensate has been 
removed from the receiver in this case, there are unequal weights 
of steam in the two cylinders during the respective expansions, 
consequently saturation line S'S' lies to the left of SS. 

Fig. 226 also shows the quality curves xn and Xi, which are 
obtained, after the saturation lines have been drawn, by the same 
method that was described for simple engines. 

* There are several different kinds of diagram factors, each of which may be 
used to best advantage for some particular purpose. When the engine is consid- 
ered by itself, the definition previously used in the text is the one most commonly 
given. The A. S. M. E. Report of Committee on Standardizing Engine Tests 
defines the card factor in such manner as to include the cylinder-feed losses be- 
tween engine and boiler. See Trans. A. S. M. E., Vol. XXIV, page 751. 




CHAPTER XXI. 

PERFORMANCE OF STEAM ENGINES. 

177. Steam Consumption, (a) Steam engines are governed 
by (i) throttling the steam, (2) by varying the cut-off, and 
(3) by combining (i) and (2). 

When the engine is governed by throttling (the cut-off re- 
maining constant), the available energy AE per pound of steam 
theoretically decreases as the pressure is reduced. This is shown 
in the Mollier diagram, Fig. 227. Starting with initial pressure 
pi, the associated heat A(2i, and back 
pressure pb, the available energy is 
A£i. In throttling to pressure p2 the 
associated heat remains unchanged, 
but the available energy per pound 
is reduced to AE2, and consequently 

Fig. 227. more steam, in the ratio (-te^), must 

be used to develop one i.h.p.-hour. Evidently the actual throt- 
tling engine gives the best economy only under maximum load, 
hence the water-rate curve will resemble cd in Fig. 228. 

It is found that with this type of governing, the curve of 
total consumption {ah) is practically a straight line, and this 
relation is commonly called Willans' Law. When two points 
on this line, or one point and the slope, are given, the line can 
at once be drawn. Then dividing ordinates by corresponding 
abscissas gives the simultaneous values of the water rate, and 
these values can be used for plotting the water curve. 

With greater ratio of expansion, less steam is used for a given 
output, hence for such cases the curves a'h' and c'd' in Fig, 228 
would lie below the others. 

(b) When the engine is governed by varying the cut-off, the 
water-rate curve resembles efg in Fig. 229, the reasons for which 
were made clear in Section 125. To this figure has been added 

352 



PERFORMANCE OF STEAM ENGINES 



353 



the curve cd of Fig. 228, the point d of course coinciding with g. 
Thus it is seen that cut-off governing gives better results than 
throttle governing except at the maximum load. 

The product of abscissas by ordinates gives the total steam 
consumption, plotting which gives the curved line hij as the 
Curve of Total Water Consumption for cut-off governing. Evi- 
dently point i, where a line drawn from becomes tangent to 
hij, determines the abscissa for the lowest water rate, for that 
point has the smallest ratio of ordinate to abscissa. 

(c) The y intercept Oy of the T.C. curve represents the weight 
of steam used when no i.h.p. is being developed. It is the weight 
which furnishes heat equivalent to the losses from condensation, 
leakage, and radiation. 

Curves similar to Figs. 228 and 229 might have B.t.u. as ordi- 
nates; and m.e.p's, cut-offs, ratios of expansion, or d.h.p's may be 





Fig. 228. 

used as abscissas. When abscissas are d.h.p., then the y inter- 
cept represents the consumption due to engine friction in addi- 
tion to the other losses mentioned in the preceding paragraph. 

(d) If, in Fig. 229, 00' is the i.h.p. used in overcoming the 
engine friction, then O'Y' is the axis from which the d.h.p. are 
measured. If the engine friction is assumed constant for all 
loads (which is not strictly true), the curve TC in the figure, 
with origin at 0' , gives the total consumption for the d.h.p. de- 
veloped. The curve e'fg' of water rate per d.h.p. -hour will of 
course lie above efg, and the lowest point /' will lie farther from 
than /. Evidently, on the basis of delivered power, the best 
economy in this case occurs when the i.h.p. equals Ok' (corre- 
sponding to a d.h.p. of O'k'), and this should be the power which 
the engine normally develops (" Normal Power ") if steam econ- 
omy is of prime importance. This should then be the " rated 



354 HEAT-POWER ENGINEERING 

power," or power at which the engine is rated to operate nor- 
mally. When the i.h.p. developed is either more or less than 
this, the engine has poorer economy. 

(e) The load factor is the ratio of the actual load to the 
rated load. There are instantaneous load factors, and average 
load factors. For best steam economy the load factor should be 
unity; and, since it is better to overload than to underload a 
steam engine (see Fig. 229) , a load factor a certain amount above 
unity is preferable to one the same amount below. There are, 
however, other considerations which may make it financially more 
profitable to rate the engine at output other than that giving 
best steam economy, and to operate with some load factor other 
than unity. 

In many instances, the average load factor of the power plant 
as a whole is low, but in such cases it is customary, when pos- 
sible, to have several engines and to place in operation such a 
number as will cause those in service to operate under the most 
economical conditions; that is, the load factors of the individual 
engines are maintained near unity. 

The instantaneous load factor may vary widely, as in a street- 
railroad power plant, and the fluctuations may be of such rapid 
character as to prohibit changing the number of engines. In 
such a case a small average load factor may be unavoidable. 

(f) Curves of steam consumption for an engine are useful in 
determining the best conditions of operation for that particular 
engine and for comparing it with others that operate under 
similar conditions. When the conditions are widely different 
the water rates should not be compared directly. 

To reduce water rates to a comparable basis, when the differ- 
ence in conditions of operation is not great, the following cor- 
rections may be made : * 

0.4 to 0.6 per cent per i inch change in vacuum (between 25 
and 28 inches). 

I per cent per 8 to 11 degrees of superheat (at from 50 to 
100 degrees). 

0.1 to 0.2 per cent per pound of initial pressure. 

I per cent per i per cent of moisture. 

The only true comparison is on the basis of B.t.u. per h.p. 
per unit of time (minute) or on the basis of thermal efficiency 
* Moyer's Steam Turbines, page 288: — Wiley & Sons. 



PERFORMANCE OF STEAM ENGINES 



355 



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356 



HEAT-POWER ENGINEERING 



on the d.h.p. The engine having the lowest water rate and the 
highest cyHnder efficiency does not always use the least heat per 
unit of power, nor have the highest thermal efficiency. 

178. Steam-Engine Performance: Data. — (a) The perfor- 
mance of engines is dependent on many things, of which the 
more important ones are: (i) initial pressure, (2) back pres- 
sure (condensing, noncondensing), (3) cut-off, or expansion ratio, 
(4) number of expansion cylinders, (5) quality, or superheat, 
(6) use of jackets, (7) use of reheating receivers, (8) speed, and 
(9) the proportions, size, and arrangement of cylinders, clear- 
ance spaces, and passages. These items must be considered in 
comparing economies. 











1 








— = Nonrcondensing 

- = nnnflensino- 






250 














= Superheated and Condensing 

+ = Single Valve-Simple 
• ;=■ Four Valye -Simple 

A = Triple 








r\ 






5' 200 

1 








A 






\ 


B= Bit 
J = Ja 
R=- Ke 


feLd 










^ 






\ 


\ 










1 

|150 








^ 


,4\ 




\ 




\ 














'} 


If ^ 




\ 


V5 


\ 








|ioo 








J 


J \ 

1 




J 


f 


^ 


A 
\\ 












\ 
\ 




u'— 


v-^' 


^ ^ 


~^' 


--* 


\ 




50 








\ 
\ 
\ 






H 


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■h—*-' 














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iluusiu 
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s 






^ 


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sius 
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.t.u. I 


3{ 
erI.F 


[.p. PC 


4( 
r Min 


K) 


5( 


W 


60 



Fig. 230. 

Table VII is a brief summary of Gebhardt's more extensive 
tables,* with a few additions and omissions. It will serve as a 

* See Gebhardt's "Steam Power Plant Engineering," pages 296, 306, and 314. 
Wiley & Son, publishers. 

Also Heck's "The Steam Engine," Vol. II, pages 600-652. 



PERFORMANCE OF STEAM ENGINES 



357 



rough comparison of some of the best performances that have 
been obtained with the principal types of engines. The condens- 
ing, multiple-expansion engines are in most cases steam- jacketed 
unless the steam is superheated. 

Although the tabulation as here given does not bring out this 
point, it should be remembered that while the lowest B.t.u. 
per i.h.p.-min. corresponds to the highest thermal efficiency, it 



r 



+ = Single Valve-Simple 
Four Valve — Simple 
Compound B ^Binary 

Tiiple J— Jacketed 

□ = Quadruple R = Regenerativ 



= Non-condensing 

= Condensing 

= Superheated and Condensing 




10 12 14 16 18 20 
Thermal Eff. on the I.H.P 



Fig. 231. 



does not follow that it is accompanied by low water rate and 
high cylinder efficiency. 

(b) Figs. 230 and 231 show respectively the variations of 
B.t.u. per i.h.p.-min. and the thermal efficiency on the i.h.p., 
with initial and exhaust pressure, with superheat, with type of 
engine, etc. Reference to these figures shows that, as compared 
with the Clausius cycle with 28-inch vacuum, the losses of 
various types of real engines are about as follows in the best 
condensing practice: 



358 HEAT-POWER ENGINEERING 

Quadruple 20% 

Triple 25% 

Compound 33% 

Simple 50% 

(c) Table VIII gives a brief summary of steam-engine efficien- 
cies, including some of the best. Table IX gives the pounds of 
steam consumed per i.h.p.-hour by ordinary engines which op- 
erate under the usual commercial conditions and in which no 
special provision is made for improving economy — such as super- 
heating, jacketing, etc. Larger engines, of course, give better 
results than smaller ones. 

TABLE VIII. — SUMMARY OF EFFICIENCIES OF STEAM ENGINES. 

Carnot cycle efficiency * 10 to 32% 

Clausius cycle efficiency * 8 to 28% 

Indicated efficiency 40 to 88 . 2% 

Theimal efficiency on i.h.p 5 to 25 . 05% 

Mechanical efficiency 85 to 97% 

Thermal efficiency on d.h.p 4 to 23 . 9% 

Over-all efficiency 35 to 84% 

Heat used per i.h.p.-min 169 . 3 to 700 B.t.u. 

TABLE IX. — STEAM CONSUMPTION. 
Type of Engine. Lbs. i.h.p.-hour 

Simple " high-speed " engines (non condensing) 28 to 36 

Simple Corliss engines (noncondensing) 25 to 28 

Compoimd slide-valve engine (noncondensing) 24 to 26 

Compound slide-valve engine (condensing) 15 to 21 

Compoimd Corliss engine (condensing) 14 to 16 

Triple-expansion (condensing) i2f to 13 

* Obtained from Figs. 73 and 75 respectively with the following assumptions: 
The lower limit of pi is assumed at 50 pounds pressure and fc = 212° F. The 
upper limit of pi is assumed at 150 pounds pressure and ti = 100° F. 



CHAPTER XXII. 

STEAM TURBINES. 

179. Introductory, (a) The earliest steam-driven prime mover 
recorded in history is Hero's steam turbine (about 200 B.C.) , which 
is shown in Fig. 232. It was a "reaction turbine," driven by the 
repulsive force produced by a jet of steam issuing rearwards as 
regards the direction of rotation. Branca's "impulse turbine" 





Fig. 232. Fig. 233. 

(1629), shown in principle in Fig. 233, is the next historical refer- 
ence to the use of steam in a turbine. The first patents in 
foreign countries appeared about 1820 and the primary patent 
in the United States was issued in 1831. Although many steam 
turbines were invented in the succeeding years, it was not until 
the latter 80's of the last century that the modern commercially 
successful types began to be developed. 

(b) A steam turbine may be defined as a device in which one 
or more jets of the working substance moving at high velocity 
(and therefore possessing kinetic energy) act or react on vanes 
or buckets on one or more wheels, or drums, in such manner as 
to cause them to rotate and transmit power by means of the 
shaft on which they are mounted. 

The shaft, the wheels or drums, and their attachments con- 
stitute the "rotor." The working substance is steam, which 
may have moisture entrained in it. The velocity of the jet is 
acquired by the expansion of the steam through a nozzle, or its 
equivalent, during which process some of the heat energy of 
the steam is converted into the kinetic energy of the issuing jet. 

359 



360 HEAT-POWER ENGINEERING 

In "impulse turbines" the nozzles are stationary and the jets 
act on the turbine vanes; in the "reaction" type, the nozzles, 
or their equivalents, are mounted on the rotor, which is driven 
by the reaction of the jet. In some turbines the rotors are 
driven by both impulse and reaction. 

(c) The velocity diagrams used in designing the buckets of 
the steam turbine are similar in many respects to those used 
for water turbines. But, despite this resemblance, the problems 
of design and construction in the former differ greatly from those 
in the latter. This is principally because, in the steam turbine, 
(i) the jet velocities are enormously greater (in some cases this 
velocity exceeds 3600 feet per second, or 41 miles per minute), 
(2) the bucket velocities are very much higher, (3) the working 
substance is elastic and tends to expand as fully as the surround- 
ing media will allow, and (4) because the kinetic energy of the 
jet is obtained from heat conveyed by the working substance 
and not from "hydraulic" head. 

(d) The steam turbine differs as much from the steam engine 
as to its mechanism and method of operation as does the water 
turbine. Although both of these steam-actuated prime movers 
use the available heat of the steam, the turbine utilizes it in 
increasing the velocity (kinetic energy) of the jet of working sub- 
stance, whereas this heat in the steam engine produces certain 
pressure-volume changes within a cylinder. 

(e) The thermodynamic problems encountered in the steam tur- 
bine are centered in the nozzle, where (theoretically) all the heat- 
energy transformations occur. After the jet has issued from the 
nozzle end the problem becomes a dynamic one, namely, to con- 
vert the jet's kinetic energy into power which can be delivered 
by the shaft. 

The problem of nozzle design and the thermodynamic theory 
involved will be considered in detail in a later chapter. For 
present purposes it is only necessary to know that high veloc- 
ity can be attained at the expense of associated heat and that 
this transformation occurs entirely within the nozzles or their 
equivalent. 

(f ) In turbines, there is a certain definite ratio of bucket velocity 
to jet velocity that will theoretically give the best economy. In 
practice, however, if the full expansion from initial to final pres- 
sure takes place in a single set of nozzles, the bucket velocity for 



STEAM TURBINES 



361 



best economy is usually greater than the structure of the rotor 
will stand, because of the enormous centrifugal force produced. 
Also, the high rotative speed involved with high bucket speeds 
usually prohibits the direct connection of the driven machinery 
to the turbine shaft. Hence, if the expansion occurs in a single 
set of nozzles, it is usually necessary to use lower bucket veloci- 
ties than those which would give the highest economy, and also 
to use gearing of some kind between the turbine and the machine 
it drives. 

In order to obtain lower jet and bucket velocities, most 
turbines are of the "multi-stage" type. Fig. 234 shows dia- 
grammatically an impulse turbine of this type. In such tur- 
bines each stage by itself constitutes a simple turbine, in the 
nozzle of which the steam expands through a small range and 
therefore acquires relatively low velocity. The stages are usu- 
ally arranged in series with diaphragms between and with all 
rotors mounted on the same shaft. 

In Fig. 234, the sections of the turbine casing and the dia- 
phragms are shown by crosshatching, and the nozzle and tur- 
bine wheel sections are black. 
Steam enters at the left, ex- 
pands through the first nozzle 
(or ring of nozzles) Ni, in 
which it acquires a relatively 
low velocity, and discharges [XJ 
against the buckets on the 
wheel in the first-stage casing, 
in which the pressure is but 
little lower than the initial. 

The steam then expands through the nozzle (or ring of nozzles) 
Ni, in the diaphragm between the first and second stages, and 
acts on the buckets of the wheel in the second chamber, where 
the steam pressure is somewhat lower than it is in the first stage. 
In similar manner the process is continued in a third stage, and 
in many instances in from twenty to forty stages, until the 
exhaust pressure is reached in the last, stage. 

The nozzles in all the stages must all deliver the same weight 
of working substance per second. They may be designed to do 
this with equal velocities, in which case the bucket velocities in 
all stages would be the same and the mean diameters of the 




Fig. 234. 



362 



HEAT-POWER ENGINEERING 



wheels would be equal ; or the jet velocities may be varied and the 
bucket velocities and wheel diameters be made to correspond. 

As the steam traverses the turbine it expands by increments 
in the successive nozzles, and increases in volume, hence the 
nozzle areas must increase in like manner through the series, 
as is illustrated in Fig. 234. 

By properly proportioning the cross-sectional areas of the 
inlet and outlet nozzles of any stage, the designer can fix at 
any desired value the pressure that will be maintained in that 
stage. 



180. Thermodynamics of the Ideal Steam Turbine, (a) In 

all types of steam turbine the steam is expanded through noz- 
zles, or their equivalent, and the velocity of the working sub- 
stance itself is increased by the conversion of some of its own 
associated heat into available mechanical energy, which appears 
as the kinetic (velocity) energy of the issuing jet. As the 
nozzles, or their equivalent, are relatively small, and as the 
velocity of the steam through them is enormous, there is little 

opportunity for loss of heat, as 
such, to the surrounding media, 
or for the reception of heat, as 
such; hence, the conversion of 
heat energy into kinetic energy 
must in practice be almost 
strictly adiabatic, and it will be 
shown in a later chapter that 
the expansion may be considered 
equivalent to an isentropic pro- 
cess in the ideal case. 

(b) Assuming that the steam 
is initially wet, and that its state 
is represented by point 1 on the 
T0-diagram in Fig. 235, the heat 
(A(2i) supplied per pound of 
steam delivered to the turbine is 
represented by the area bounded 
by the bold line. Let point 2 represent the state of the working 
substance after isentropic expansion to the exhaust pressure and 
temperature. Then the hatched area represents the heat (AQ2) 




STEAM TURBINES 363 

remaining in tiie steam at the end of the process. Thus the heat 
theoretically available for the turbine to deliver as useful work is 

^E = A(2i - A(22, 

and this is shown by the stippled area, ahl2, which is seen to have 
the same boundary lines as those of a Clausius cycle, with the 
same conditions of expansion. The isentropic process from 1 to 
2 may occur in one nozzle, converting A£ into kinetic energy, or 
it may occur in any number («) of nozzles in series, each con- 
verting part of A£, but with cumulative efifect equal to that 
produced by A£ in the single nozzle. Thus, regardless of the 
number of stages, it may be said that the heat energy available 
for doing work in the steam turbine is equivalent to the ^.E avail- 
able with the Clausius cycle having the same expansion line and 
same weight of steam. The value of A£ per pound may be 
computed by the method given on page 173; or it can be ob- 
tained from the area on the T0-diagram; or it can be more 
conveniently found from the Mollier chart (Appendix). 

(c) Having determined the number of B.t.u. represented by 
A£, the steam consumption per h.p.-hour, or water rate, in the 
ideal turbirie is 

W--^ (3H) 

and if the turbine drives an electric generator the theoretical 
water rate per kilowatt-hour is 

^^ 0.746 ^E A£ ^^^^ 

(d) The actual turbine of course has a poorer (larger) water 
rate than the ideal. If Wd is the actual water rate per h.p.- 
hour delivered by the turbine shaft, and WdK is that per kilo- 
watt-hour delivered by the generator, then the over-all efficiency 
of the turbine (alone) is 

0£/.= ^, (316) 

and the over-all efficiency of turbine and generator is 

The OEfd corresponds to the OEf of the steam engine (p. 190). 



364 



HEAT-POWER ENGINEERING 



If it is desired to estimate the probable performance of a 
turbine, and the OEf is known for similar turbines under similar 
conditions of operation, the probable water rate per d.h.p.-hour 
is, from Eqs. (314) to (317), 

Wa = 2545 -^{AEX OEf,), . . . , (318) 
and per kilowatt hour it is 

W,K =- 3411 - (A£ X OEJk) (319) 

In very large turbo-generator outfits the value of OE/k should 
be 0.65 or more. In general the smaller the turbine the poorer 
the eflficiency, as is shown in a very general way in Fig. 236. 
70 




2000 40U0 

Kw. (Full Load) 

Fig. 236. 

(e) The ultimate comparison of the performances of turbines 
with each other and with steam engines is either on the basis of 
B.t.u.'s supplied per minute per unit of output, or on the basis 
of thermal efficiencies. In the ideal turbine the B.t.u. supplied 
per h.p. per minute are 

Bi = Wi (qi + Xiri + CpDi — q^) -4- 60, 
in which q^ is the heat remaining in the condensate, which heat 
is considered as being returnable to the boiler with the feed 
water (as in Seci. 115 (d)). In the actual case the B.t.u. sup- 
plied per d.h.p. per minute are 

Bd = Bi/OEfd = Wd(qi + xin + C,Dr - q,) - 60. (320) 
The B.t.u. supplied per kilowatt per minute in the ideal case are 
BiK = WiK (qi + Xiri + CpDi - q^) H- 60, . . (321) 
and in the actual case 

BdK = Bik/OE/k = WMQi + xir, + C^Di - q^) ^ 60. (322) 
The values of BdK vary from 250 to 800 B.t.u. per minute. 



STEAM TURBINES 



365 



(f) The ratio of the heat delivered as useful energy to that 
supplied in the steam is the thermal efficiency. The thermal 
efi&ciency on the d.h.p., as in the case of the steam engine 
(page 210), is 

2545 ^ 2545 

60 XBd 



TDEf 



Wd (qx + x,n + Cj,D, 
and based on the kilowatt output it is 

_34iL__ = 341 1 

60 X BdK 



Q2) 



(323) 



TDE/k 



(324) 



WdK (21 + xiri + CpDi — 22) 
(g) Fig. 237 shows typical curves for a large turbine-gener- 
ator outfit. It is seen that the curve of total steam consump- 




1000 2000 3000 4000 

Kilowatts at Switchboard 
Fig. 237. 

tion (T.C. curve) is practically a straight line; and this is a char- 
acteristic of such curves for nearly all types of turbines. If, in 
the figure, the T.C. curve is extended to intersect the Y-axis, the 
intersept (Fo) represents the steam required to operate the 
turbine when delivering no power. It is the amount needed to 
overcome the friction of the turbine and the " windage " (or 
friction between the turbine disks and the vapor in which they 
rotate), that required for driving the governor, oil pumps, etc., 
and that for meeting the losses due to leakage and radiation. 

The water-rate curve (W.R.), or curve of steam used per kilo- 
watt hour, is also shown in Fig. 237. The water rates at the 
different loads are obtained by dividing each total consumption 
by the corresponding kilowatts as found by test, i.e., by dividing 



366 HEAT-POWER ENGINEERING 

the ordinates of the T.C. curve by the corresponding abscissas. 
If the T.C. curve passed through the origin, as it would in the 
ideal case, the W.R. curve would be a horizontal straight line, 
and the economy of the turbine would be the same at all loads. 
The greater the Y intercept of the T.C. curve the more curva- 
ture does the W.R. curve have, and the greater are the consump- 
tions of steam under light loads [as compared with those under 
heavy loads. It will therefore be noticed that the best economy 
is obtained when the turbine is operated at its maximum power. 
As a turbine when operating under its usual load should have 
some reserve power (or " overload capacity "), it must normally 
'Operate at a load and an efficiency less than the maximum. On 
this account, and because wide fluctuations of load may occur, 
a flat water-rate curve is desirable. 

Many turbines have an auxiliary " overload valve " which 
admits live steam to the low-pressure stages of the turbine when 
it is considerably overloaded. At such load the T.C. curve and 
W.R. curve change character, as in Fig. 237 at and 0'. 

In Fig. 237 is also shown the curve of over-all efficiency of 
turbine and generator {OEJk). In this case A£ has been taken 
as the available heat in the steam just before it reaches the 
throttle valve. Thus OEJk includes the losses entailed by the 
governor valve throttling the steam, which is the principal 
reason for the decrease of this efficiency when the turbine output 
is diminished. Why this loss occurs is explained in (k) of this 
section. 

(h) Fig. 238 shows on a M oilier chart an expansion line 
starting with dry saturated steam at p pounds pressure and 



Fig. 238. 

-extending to various lines of terminal pressure. It is seen that ex- 
pansion to 15 pounds pressure theoretically makes available heat 
represented by a, and that further expansion to one-half pound 
absolute back pressure would add to this an amount of heat 
represented by g. Thus, if steam from an ideal noncondensing 
•engine or turbine is expanded in a second ideal turbine to one- 



STEAM TURBINES 367 

half pound absolute pressure, the total power obtainable would 
evidently be nearly twice (in this instance) that derived from the 
noncondensing unit. Many "low-pressure" or "exhaust-steam" 
turbines are operated with steam received from an engine at 
about atmospheric pressure, and these in many instances give 
as much power as do the engines which furnish the steam. 

Again referring to the expansion Hne in Fig. 238, and starting 
with terminal pressure 2| lbs., it is seen that the succeeding half- 
pound drops are accompanied by the heat increments lettered 
c, d, e, and /, the amounts of which, in this particular case, in- 
crease the available energy respectively in the percentages 4.7, 
5.6, 6.3, and 10. It is apparent that these heat increments rapidly 
become larger as the back pressure is lowered, hence a one-inch 
change in vacuum from 28 to 29 ins. is much more effective than 
one from 26 to 27 ins. The actual case would, of course, differ 
somewhat from the ideal, but the real gains from improving the 
vacuum are about proportional to the theoretical; hence, with 
steam turbines, it is desirable to use as low back pressures as the 
other considerations will permit. 

(i) In the T0-diagram in Fig. 239 the Clausius cycle is super- 
imposed on the Rankine, ge being the constant volume line at 
release in the latter. Now, by de- 
creasing the back pressure, with tem- 
perature reduction from T2 to T3, the 
increased amount of heat made avail- 
able in the ideal turbine is shown by 
area abed, whereas in the engine it is 
only aefd. Actually there is still 
greater difference between the gains, 
for in the engine the increased range 
of temperature augments the loss due p. 

to cylinder condensation, whereas in 

the turbine there is no equivalent to such condensation since 
the steam flows continuously in the same direction, and there- 
fore constantly comes in contact with parts which have pre- 
viously become heated to its own temperature. Evidently, 
then, the turbine can use very low back pressures to better 
advantage than the engine, other things being equal. 

(j) The gain due to using superheated steam is illustrated on 
the Mollier chart in Fig. 240. In expanding from dry satu- 





368 HEAT-POWER ENGINEERING 

rated steam at p pounds pressure to 1 pound pressure, B.t.u. 
represented by AE are seen to become theoretically available, 
whereas in expanding through the 
same pressure range but starting 
with steam superheated 150 de- 
grees, B.t.u. represented by AE' are 
made available. If pis 165 pounds 
absolute, a gain of nearly 1 1 per cent 
^^" "®^ is effected per pound of steam, and 

Fig. 240. only about 0.9 as much steam would 

be used as with saturated mate- 
rial. The gain in fuel economy is not in this proportion, how- 
ever, as additional heat was supplied per pound of steam in 
superheating it. The heat (above 32 degrees) of 1 pound of the 
superheated steam is seen to be 1277 B.t.u., and in the case 
of the saturated steam it is 1195. If the feed water is at 72° F., 
it contains about 40 B.t.u. above 32 degrees. The fuel used per 
pound in the two cases will then be in the ratio (1277 — 40) -^ 
(i 195 — 40) = 1.07. Thus the heat supplied by the fuel per unit 
of work when superheated steam is used is 0.9 X 1.07 = 0.96 
times that needed with saturated steam, and the theoretical saving 
in fuel is 4 per cent in this instance. The actual saving may be 
greater than this, for superheating results in the steam having 
less moisture after the adiabatic expansion, and the presence of 
moisture somewhat increases the friction that the steam en- 
counters in passing over nozzle and blade surfaces. 

In the steam engine, superheating may effect greater improve- 
ment in economy than occurs in the turbine, because of its influ- 
ence in preventing cylinder condensation. 

(k) It is quite common practice to decrease the power output 
of a turbine by throttling the steam supply. This process not 
only reduces the amount of steam, but 
lowers its pressure and changes its 
entropy in such manner that the heat 
available per pound with any fixed 
terminal pressure is reduced despite ^i-^^i 
the fact that the total heat of the steam '^' ^'^^' 

remains the same. This is illustrated in Fig. 241, in which AE is 
the heat available per pound of steam before throttling, and 
AE' is that after throttling, the total heat AQy of the steam being 




STEAM TURBINES 



369 



initially the same in both cases. It is therefore evident that the 
throttling process must theoretically decrease the economy of the 
turbine. 

181. Thermodynamics of Actual Turbines. In the energy 
stream of Fig. 242, A£ is the heat that would be made available 
for doing work when there is complete expansion of i pound of 

Avail able Energy 

TA A ^ A A A^ 

1 C B E F G 




Fig. 242. 



steam through the nozzle, or nozzles, of a single stage of an 
ideal turbine, and A(22 is the unavailable, or waste, heat. 

(a) In the actual case, some of the steam may not pass through 
the nozzle, for there may be leakage to the exhaust. For ex- 
ample, in Fig. 234 some of the steam may leak from chamber 2 
to chamber 3 through the clearance space a between the third 
diaphragm and the shaft. This leakage loss (which may repre- 
sent from zero to 5 per cent, or more, of the total energy) is shown 
by stream line a in Fig. 242, and the energy still available for 
doing work is represented by A . 

(b) Because of the frictional resistance offered by the nozzle 
walls, and because of eddy currents, etc., all of the heat theo- 
retically made available by the steam expanded through the 
nozzles is not converted into kinetic energy of the jet. The 
portion of AE not utilized remains in the steam as heat; hence 
in the figure the nozzle loss h is shown as subtracted from the 
available energy and added to that wasted. This loss may be 



370 HEAT-POWER ENGINEERING 

from 3 to 15 per cent of the total available energy. The energy- 
still available is shown in the figure by B. 

(c) Similarly, not .all of the kinetic energy of the jet is ab- 
stracted by the turbine buckets. The remainder, or bucket 
loss, which may be from 10 to 30 per cent, is reconverted into 
heat by eddy currents and by the reduction of velocity in the 
turbine chamber, and this heat is added to that already in the 
steam before it reaches that point. This loss is represented by 
c in the figure, and the energy still available, by C. 

(d) Further, because of the " windage," or friction between the 
rotor and the enveloping vapor, not all of the energy absorbed 
by the buckets is transmitted to the turbine shaft. This loss 
may be from 2 to 8 per cent with the high velocities of rotation 
prevailing. This frictional energy is converted into heat by 
the eddy currents set up in the vapor, and this heat is added 
to that already stored in the vapor, as shown at d in the figure. 
The energy still available for doing work is shown by D. 

(e) The heat not utilized remains in the steam and is shown 
by H in the figure. If the steam from this casing is used in 
another turbine, or as another stage of the same turbine, the 
diagram of energy flow for this second element would also resem- 
ble Fig. 242, but the initial width of the steam line would be H, 

(f) In addition to the foregoing, there are the radiation loss 
and the mechanical losses from bearing friction and (possibly) 
from the driving of oil pumps, governor, etc. These are shown 
at e, f, and g. G represents the energy finally delivered by the 
shaft. The ratio of G to AE is the over-all efficiency of the 
turbine * (not including the generator) . 

(g) Losses a, b, c, d, and e constitute the equivalent of the 
cylinder losses in the steam engine; hence, the ratio of the heat 
shown at E to A£ may be called the cylinder efficiency (/£/). 

(h) Fig. 242 will also apply qualitatively to multistage tur- 
bines considered as a whole, in which case a, b, c, d, and e show 
the combined losses of all stages. 

(i) On the MoUier chart in Fig. 243, let the initial state of 
the steam be shown by point 1, with pressure pi, entropy 0i, 
quality Xi, and associated heat AQi per pound. In the ideal 
case, after expansion through the nozzle to a pressure of p2 
pounds per square inch, the state point would be at 2, with 
* This is sometimes called the "shaft efficiency." 



STEAM TURBINES 



371 



entropy 0i, quality X2, and associated heat A(22. The heat theo- 
retically made available is shown by A£. In the real case, 
as has been seen, only a part of A£ is actually delivered to 




Fig. 243. 

the shaft by the wheels or drums. This amount is shown by 
AE' = (/£/ X A£) in the figure. Evidently the heat remaining 
in the exhaust steam is shown by AQ2 = (A(2i — AE'). 

With this amount of heat in the exhaust steam and with the 
terminal pressure P2 as before, the state point showing the con- 
dition of steam in the actual case must be at 2' , the point on 
the pressure line having heat value equal to AQ2 . Thus the 
actual condition of the exhaust steam is such 
that the quality is X2 , the entropy is </)2, and 
the heat above 32 degrees is ^Q^' . This is 
the condition of the steam exhausted to the 
condenser or to the atmosphere, or to the 
next stage, as the case may be. 

(j) Fig. 244 is a T0-diagram correspond- 
ing to the Mollier chart in Fig. 243 and is 
similarly lettered. A(2i is shown by the area 
bounded by heavy lines, i^Q^ by area Oab24>i, 
and AQ2 by the hatched area. AE' is the 
difference between the areas AQi and AQ2 and is not shown 
directly by any area on the diagram. 

182. The Dynamics of Impulse Steam Turbines, (a) In dis- 
cussing the dynamics of turbines, it is necessary to distinguish 
between the " absolute " velocity and the " relative " velocity 
of the jet of steam. Absolute velocity is the linear speed (v) of 
the jet with respect to things that are stationary; the relative 
velocity (R) is the speed of jet relative to the buckets, which 
themselves are moving with a velocity u. 




Fig. 244. 



372 HEAT-POWER ENGINEERING 

(b) The available energy of w pounds of steam flowing through 
the nozzle per second is w X 778 X AE, and the kinetic energy 
which it imparts to the jet is 

KE = ^, (325) 

in which v is the absolute velocity of the jet in feet per second. 
Hence, if the nozzle efificiency is £/„, 

Efn X w X 77S X AE = — , 
from which the velocity of the jet is found to be (feet per second) 



V = 223.8 V A£ X E/„ (326) 

(c) To completely utilize the kinetic energy of the jet in an 
impulse turbine, the absolute velocity of the jet must of course 
be reduced to zero (regardless of the final direction of motion), 
and it is the function of the blades on the rotor to perform this 
reduction and receive the energy. If, after passing over the 
blades, the jet still has velocity (^2), it is evident that there is 
loss of energy due to the residual velocity equal in amount to 

■ KE.-"^ (3.7) 

(d) If in Fig. 245 the jet has an absolute velocity v\ and the 
bucket has an absolute velocity u = Vxl2 in the same direction, 

the relative velocity of jet to bucket is 
R = 2^1/2 as it enters. Then if the 
bucket directs this jet rearwards (op- 
posite and parallel to z;i), the absolute 
velocity v^ of the working substance is 
zero, and the entire energy has been 
absorbed. 

Could the friction between the jet 
and the surface of the bucket, the eddying, and spilling of the 
working substance, be eliminated, the efficiency of conversion in 
such a case would be 100 per cent. 

(e) If in Figure 246 the line / represents the absolute velocity 
Vx of the jet and its direction of motion compared with that of 
the bucket, the direction and velocity of which are shown by u, 
the relative velocity of jet to bucket is shown in amount and 
direction by i?i, which is found by constructing the triangle 




STEAM TURBINES 373 

nhc with side be = u. If i?2 is the relative velocity and direction 

in which the jet is discharged with re- «,^^ 

spect to the moving bucket, then V2 is ^^>^<L 

the absolute velocity and direction of the / R>\^"^^^^.,^ 

jet, and its vector is found by con- —i N ^ n ^ , j , 

structing the triangle def with side ^^ — - — ^ 

ef = u. Evidently the presence of this ~~\ ^// ^ ''^^' 

residual velocity Vz represents, a loss V/'^/^'a 

of energy which is equal to zW2^/2 g. ^^^^ J 

Hence the bucket efficiency, neglecting i' ^ 

other losses, is Fig. 246. 

_ lim^ _ imf\ _^ im^ _ Vx" - v^^ . . 

^^-[2g 2g) ■ 2g- v,^ • • • ^^^^^ 

It will be apparent from Fig. 246 that V2 can never be made 
zero if Vi and V2 are not both parallel to u, and that unless this is 
the case the bucket efficiency must be less than unity. It will 
also be evident that Vo is a minimum, and the efficiency is maxi- 
mum, when u is of such value as to cause v^. to be at right angles 
to ti. This value of v can be determined either graphically or 
mathematically by methods which need not be considered here. 
If angle abc = 20°, which is about as small an angle as can be 
used when the nozzle is placed at the side of the buckets, and if 
i?i and R2 form equal and opposite angles with the direction of 
the bucket's motion, u will be about 47 per cent of Vi. 

Further discussion of the dynamics of turbines will be given 
in connection with the descriptions of the various types. 

183. De Laval Type of Single-Stage Turbines. — This type of 
turbine (developed about 1888) is shown diagrammatically at A 
in the chart given on page 374 ; and the details of its mechanism 
are shown in Fig. 247. The velocity diagram resembles Fig. 246, 
but as the velocity (^i) of jet issuing from the nozzle may be 
from 3000 to 4000 feet per second, it is not usually possible to use 
bucket velocities (u) which correspond to maximum efficiency, 
for no available materials or possible constructions will withstand 
such speeds. The bucket velocities are therefore made as high 
as is safe. The wheels of the 300-horse-power De Laval turbine 
are about 30 inches in diameter and rotate at about 10,600 r.p.m., 
with peripheral speed of about 1380 feet per second. The 



374 HEAT-POWER ENGINEERING 

CHART. — Principal Commercial Types of Steam Turbines. 



Initial /yT7»^^^H Exhaust 
Pressuce ((.N . 




Nozzle Blades 



A. De Laval Type. 




stages =1 2 3 4 5 

B. Rateau-Zoelly Type. 



NOTES. 

General. In each of the above diagrams the upper portion shows a longi- 
tudinal section of the turbine, the middle of the figure represents a transverse 
section through the buckets and nozzles, and below this are curves which 
show how the pressure and velocity of the steam vary during the passage 
of the vapor through the turbine. The pressures and velocities are shown 
respectively by the ordinates of the heavy and of the light curves. 

A. De Laval Type (see Sect. 183). In this type of turbine it is to be par- 
ticularly noted that the full drop in pressure and the entire increase in velocity 
of the vapor are completed before the jet issues from the end of the nozzle, 
as shown by the curves; thus there is no expansion of the steam after it 
reaches the wheel casing. The velocity curve also shows the jet's velocity- 
decrease resulting from the absorption of the kinetic energy by the buckets, 
and further shows the residual (lost) velocity associated with the kinetic energy 
not utilized. 

B. Rateau-Zoelly Type (see Sect. 185). Each pressure stage is seen to 
resemble a single-stage turbine of the De Laval type. 



STEAM TURBINES 375 

CBAKI {Continued). — Principal Commercial Types of Steam Turbines. 




1st, Stage 2ud Stage 

C. Curtis Type. 




D. Parsons Type. 



NOTES {Continued). 

C. Curtis Type (see Sect. i86). The diagram shows a turbine having two 
pressure stages, each of which has two velocity stages. It is seen by the curves 
that the pressure-drops and velocity-increases occur entirely within the noz- 
zles iVi and Ni (i.e., there is no expansion of the vapor in the wheel casings). 
In each pressure stage the jet first passes over the moving blades Mi to which 
it surrenders part of its kinetic energy (thereby losing some of its velocity), 
and is then guided by the stationary blades 5 to act on the second set of mov- 
ing blades M2, which absorb still more of the energy by further decreasing the 
velocity of the jet. Thus the (kinetic) velocity energy is absorbed in two 
steps, or stages, in each pressure stage. 

D. Parsons Type (see Sect. 188). Expansion takes place in both the station- 
ary and the moving blades, as is shown by the steam-pressure line in the dia- 
gram. The steam is accelerated in passing through the first row of stationary 
buckets; the issuing jets are then retarded by coming in contact with the first 
moving buckets, to which they surrender part of their kinetic energy; and 
while passing between these latter buckets the stream is further expanded and 
issues from them with a reaction. Thus the moving blades receive energy 
by both impulse and reaction. This process is continued in each of the suc- 
ceeding pairs of stationary and moving sets of blades. 



376 HEAT-POWER ENGINEERING 

5-horse-power turbine has a wheel about 4 inches in diameter, 
the r.p.m. are 30,000, and the rim speed is 515 feet per second. 

To provide the maximum theoretical strength, the smaller 
wheels have sections resembhng that in Fig. 247 at (o); while 
the larger wheels are without central hole, the shaft being made 
in two parts, each fastened to the side of the wheel by flanges. 
The buckets and the method of attaching them to the wheel 
are shown at {h) in the figure. The flanges on the bucket tips 
form a continuous " shroud ring," and this prevents the jets 
from flattening and " spilling " over the ends of the blades. 

Although the wheels are balanced with the greatest care, the 
gravity axis never exactly coincides with the geometrical axis 
of the shaft. To prevent difficulty which might arise with such 
high speeds from this lack of balance, the shaft is made slender 
and flexible so that the wheel can " gyrate " about its gravity 
axis. Owing to the high speed the " torque " on the shaft is 
small and a small diameter is therefore permissible. 

In most instances the rotative speeds are too great to permit 
of " direct connection " to the generator, pump, or other machine 
which is to be driven, hence reducing gears of ratio about 10 : i 
are used. 

To obtain continuity of action and noiselessness, the gears are 
of the opposed "herring-bone" type, with very narrow teeth, 
which are cut and adjusted with extreme accuracy. The pinion 
may drive either one or two pairs of large gears, each of the 
pairs delivering power independently. The power is delivered 
from the gear shaft through a flexible coupling, the bushings 
shown black in the figure being made of rubber. 

The governor shown at e is of the centrifugal fly-ball type. 
As the weights W, W, (pivoting on knife-edges at P) fly out due 
to centrifugal force, the rod R is moved longitudinally, thus 
moving the bell crank L (in view (c)) and regulating the amount 
of opening of the governor valve 5 (which is vertical on actual tur- 
bines). Thus the turbine is throttle-governed. There generally 
are several nozzles like d around the periphery of the wheel, and 
these are provided with hand-shut-off valves. If the load on the 
turbine is very small, it is better to close some of these valves, 
so that the nozzles remaining in action may operate at or near 
their maximum capacity (the most efficient condition) rather 
than have all the valves in operation with steam greatly throt- 



STEAM TURBINES 



377 




378 



HEAT-POWER ENGINEERING 




STEAM TURBINES 



379 



tied (with the 'accompanying loss). Sometimes there are two 
sets of nozzles, one to be used when operating condensing, and 
the other when noncondensing. 

184. Pelton Type of Steam Turbine. Single-stage impulse 
steam turbines, with buckets like those used on Pelton water 
wheels, may be built; but the same difficulties are encountered 
in them that appear in the De Laval type of single-stage turbine. 

By making the turbine multistage, and using a sufficient 
number of stages, these difficulties may be avoided, the jet 
velocities may be reduced to twice the bucket speeds that can 
be used safely, — thereby obtaining the highest bucket efficiency 
(see Section 182 (d)) , — and the rotative speeds may be made such 
as to permit the direct driving of electric generators, centrifugal 
pumps, blowers, etc., without the use of gearing. 

Fig. 248 shows the elements of the Kerr turbine, which is of 
this type. In this figure (a) shows one wheel, the nozzles (one 
in section), the section of the casing of the adjacent stage of 
higher pressure, and the bucket. The longitudinal section of 
the turbine is shown in (b). The steam passes from A to the 
chamber S, thence through nozzles N to the first stage, 1 , where 
the jet impinges on the buckets on the wheel, the section of 
which is shown black. From the first stage the steam passes in 
like manner through the nozzles N in the diaphragm, to act on 
the buckets of the second wheel; and so on through the turbine 
until the steam is exhausted at E. To prevent the possibility of 
any leakage of air through the stuffing boxes at B (which 
would afifect the vacuum), a chamber is provided which can be 
filled with water (forming a " water seal ") or with steam at 
pressure slightly above atmospheric. The governor and gov- 
ernor valve are somewhat similar in construction and opera- 
tion to those of the De Laval turbine. Kerr turbines are built 
only in small powers. 

185. Rateau Type of Steam Turbine. — Turbines having from 
20 to 40 stages arranged somewhat as in Fig. 234 were developed 
by Professor Rateau of Paris in 1897. The nozzles, instead of 
being of circular cross-section, are rectangular, and are grouped 
closely together so that the intervening walls are thin plates of 
uniform thickness. The buckets on all wheels, except the last 



38o 



HEAT-POWER ENGINEERING 



few, are of the same length. The group of nozzles in the first 
diaphragm extends over a short arc, that in the next diaphragm 
is a little longer, and so on ; thus as the steam passes through the 
turbine the circular arc covered by the nozzles and the passage 
areas increase in size. (See B in chart on page 374.) 

The Zoelly turbine is similar to the Rateau, except that (i) 
about half as many stages, and higher nozzle and bucket speeds, 
are used; (2) in all the diaphragms the nozzle bands extend 
farther around the peripheries; and (3) the radial widths of the 
nozzle groups, and the lengths of blades on the wheels, increase 
from one end of the turbine to the other. 



186. Curtis Type of Steam Turbine. — Referring to Fig. 246, 
it is seen that the energy loss from the residual velocity, V2, is 
quite large. Curtis (in 1896) patented the arrangement whereby 
the jet, with this residual energy, is directed to act on other sets. 
of rotating blades, from which it departs with residual velocity 
much less than in the previous case. This process is termed 
"velocity compounding." 

Theoretically, this process may be continued indefinitely, and 
the final residual velocity may be reduced to any desired value. 



Nozzles 
Moving Blades- 
Stationary Blades 
Moving Blades — »■ 



Fig. 249. 

In practice, however, the bucket fric- 
tion and other losses make it inexpedi- 
ent to use more than two or three rows 
of rotating blades per stage. Fig. 249 
shows the arrangement of a single 
stage having two rows of moving 
blades (M) , with one set of stationary 
ones (S) between, all receiving steam 
from a set of nozzles (iV) , each nozzle being controlled by a sepa- 
rate valve. Fig. 250 is the corresponding ideal velocity diagram. 
The velocities Ri, R2, and V2 are found in the same manner as in 





STEAM TURBINES 



381 



Fig. 246. The stationary blade 6" turns the discharge jet K to the 
direction /' so as to cause it to act on the bucket Aio with ve- 
locity Vs = V2 (neglecting losses). The velocity diagram v^RsRiVi 
is constructed in the same manner as in Fig. 246, and V4 is the final 
velocity, the corresponding residual energy (loss) being wv4r/2 g. 
As the steam expands fully in passing through the nozzle, the 
pressure throughout the casing of the stage is uniform. This 
and the velocity variation are shown in diagram C on p. 375. 
The smaller turbines of this type usually have but one stage, 
while the larger ones have from two to five " pressure stages " 

separated by diaphragms, 
each diaphragm containing 
the nozzles for the following 
stage. These turbines have 
either horizontal or vertical 
shafts. In the latter arrange- 
ment, which is shown in Figs. 
251 and 252, the shaft is 




Fig. 251 



supported by a " step bearing," to the center of which oil is sup- 
plied at sufificient pressure to support or float the shaft and all 
parts fastened to it. 

Fig. 251 shows diagrammatically a four-stage turbine in which 
the steam enters at the top and exhausts at the bottorn. Such 
turbines rest on a subbase, which is either connected to the con- 
denser or itself forms the walls of a surface condenser, as in Fig. 



382 



HEAT-POWER ENGINEERING 



252; the generator is placed above the turbine and the governor 
is mounted on the upper end of the shaft. Fig. 253 shows one 
arrangement of step bearing, and a portion of the rotating 



^=. --^hioud Ri 




Oil Drain 
Oil Supply 
( Under High Pressure) 



" bucket segment," with buckets held in place by " dovetails." 
The buckets are separated by " spacing blocks " and their tips 
are riveted to shroud rings. 

On large turbines the governor usually moves a small " pilot 
valve " which controls the position of a hydraulically operated 
piston, the rod of which moves a shaft having cams which open 
or close the nozzles of the first stage. Thus the power output 
of the turbine depends on the number of first-stage nozzles in 
action. The governing is by the method of " cutting out noz- 
zles " or cutting them in. 



187. Velocity Compounding with a Single Row of Rotating 
Buckets. Instead of using a second set of rotating blades in 
an impulse turbine to abstract some of the energy remaining in 
the jet when it leaves the first set, as is done in the Curtis type 
of turbine, this energy can be used (in part) by causing the 
same jet to impinge repeatedly on a single set of blades. 

Fig. 254 shows diagrammatically the elements of the " Elec- 
tra " turbine (European), which is of this type, and has blades 
perpendicular to the plane of the wheel disk. The full expansion 
of the steam occurs entirely within the nozzle N, and the guide 
passages G merely redirect the steam so as to cause it to im- 
pinge properly on the buckets. As the volume of the steam 
remains constant while passing through the guide passages, the 



STEAM TURBINES 



383 



cross-sectional area of these passages must increase as the veloc- 
ity (residual) of the steam decreases. 

The path of the jet, instead of being serpentine as in Fig. 254, 
may be helicoidal as shown at a in Fig. 255. It may be con- 




Fig. 254. 

sidered that the lower part of this path is in the semicircular 
buckets of the turbine wheel shown at b and c in the figure, and 
that the upper part is in the stationary guides of similar form. 
With this construction it is possible to obtain good steam econ- 




' Path of Jet 

a 



Fig- 2SS- 



omy with low rotative speeds, even though a single wheel be 
used. The same scheme is applicable to turbines having two 
or more pressure stages. The power that is obtainable with any 
wheel is limited by the number of nozzles and guide "blocks" 
that can be placed around the periphery. 

The forerunner of this type of turbine was the " Riedler- 
Stumpf " turbine (European), with double semicircular buckets 
like the Pelton. 

In Fig. 256 is shown a Terry turbine with casing opened. 
The method of operation is as shown in Fig. 255. Flange B 
couples to the facing 5' when the turbine is closed, and valve 



384 



HEAT-POWER ENGINEERING 




Fig. 256. 

X can be used to shut off some of the nozzles when the load is 
small. The casing is subjected to the exhaust steam only. 

The Sturtevant turbine, Fig. 257, operates in a similar man- 
ner, but is of somewhat different construction. The Dake and 
the Bliss turbines are also of this general type. 



188. Reaction Turbines, (a) A simple reaction wheel (sim- 
ilar to Hero's) is shown in Fig. 258. The pioneer developers 
(De Laval and Parsons) of the modern steam turbine and many 
other inventors have tried to produce a commercial form of 
turbine based on this principle, but without success. Experi- 
enced designers now recognize the fact that other forms are 
better for most purposes. The sectioned part a in the figure 



STEAM TURBINES 



385 




Nozzle' 
Exhaust Ports 



Fig. 257. 

constitutes a rotating nozzle of the converging type, correspond- 
ing to a small pressure drop from Pi to P2. 

(b) Another simple reaction turbine is shown in Fig. 259, with 
blades mounted on the periphery of a disk, or drum, which is 
arranged to rotate about axis XX. It is seen that the space be- 



^x 





x^ 



Fig. 258. 



Fig. 259. 



tween the blades, as shown at b, has the same form as the nozzle 
a in Fig. 258 ; hence there are as many rotating nozzles as there 
are spaces between blades. 

In this arrangement there is a " full peripheral discharge " of 
the steam around the entire circumference, and it is important 
to note that there is a difference between the pressures Pi and 



386 



HEAT-POWER ENGINEERING 



P2 on the two sides of the disk, a condition contrary to that 
present in the impulse type of turbine. 

(c) Fig. 260 may be used to show certain features of the 
modern type of reaction turbine. Between the tips of the 
blades, on the drum, and the casing there is necessarily a radial 
clearance space, and because of the inequality between the pres- 
sures Pi and Pi leakage occurs through this space. This clear- 
ance is of course always made the minimum practicable. The 
relative amount of leakage is evidently dependent on the ratio 
of this annular space to the passage area between blades; thus, 
the longer the blades are, the less the leakage, with the same 




Fig. 260. 



clearance. If the peripheral diameter is decreased, not only is 
the annular space reduced, but the blades must be lengthened to 
maintain the same passage area between them ; hence there is a 
twofold reduction in the leakage accompanying such change. 

(d) It is apparent that the difference between pressures Pi 
and P2 in Fig. 259 causes an end thrust on the shaft. The same 
is true of the arrangement in Fig. 260. This thrust may be 
resisted (i) by the thrust bearing T in this figure; or (2) by the 
balance piston B, which presents to the pressures Pi and Pi 
areas equal to those exposed by the blades and drum end; or 
(3) by using a " double-flow " arrangement of drum wherein 
there are two similar rows of blades having discharges which 
are equal but opposite in direction and hence give opposite end 
thrusts. In any case there must be a thrust bearing to main- 
tain the rotor in its proper position. 

(e) The leakage between the piston B and the shell is usually 
reduced by employing mating collars, as in Fig. 260, which 



STEAM TURBINES 



387 






Fig. 261. 

the reaction 



form a "labyrinth passage" which becomes more or less sealed 
by the moisture present in the vapor. 

(f) In Fig. 261, i?2 represents the velocity of the jet relative 
to the rotating blades, u is the blade velocity, and V2 is the abso- 
lute residual velocity of the jet. In practice 
the velocity u is rather low (usually from 150 
to 300 foot-seconds), hence the heat drop per 
stage is relatively very small. 

(g) The so-called Parsons' " reaction tur- 
bine," besides having the rotating reaction 
blades similar to those in Fig. 260, has station- 
ary guide blades which act as nozzles, the jets 
from which impinge on the rotating blades. 
Hence such turbines combine the impulse and 
principles. 

Fig. 262 shows such an arrangement, 5 and M being respec- 
tively stationary and moving blades. It is seen that not only is 

there leakage at the tips Li of 
the moving blades, but also at 
the ends L2 of the stationary 
^J\J A ones. These turbines are made 

^J%^^\^ multistage, with stationary and 

^A I^li\ I A rotating blades alternating. The 

action of the steam on the mov- 
ing blades is twofold: (i) The 
direction of the jet is changed, 
and if no other action took place 
it would leave with low velocity— 
thus there is an impulse action; 
and (2) the steam expands while 
passing through the moving 
blades and acquires velocity by 
virtue of that expansion, so that 
when discharged rearwards there 
is a reaction effect. The residual 
velocity of the jet leaving the 
rotating blade is redirected and 
increased by the next stationary blades and discharged against the 
next row of moving blades, and so on from one end of the turbine 
to the other. (See D in the chart on page 375.) 







388 



HEAT-POWER ENGINEERING 




STEAM TURBINES 



389 



As the bucket velocities are small, it is necessary to use small 
heat drops per stage, hence a great many stages are used. As 
the volume of steam under high pressure is small, the passages 
between blades must be small, and the blades themselves are 
consequently short. To reduce the leakage the high-pressure 
stages are hence made small in diameter compared with low-pres- 
sure stages, where the volume of the steam is large and the 
blades are long. The heat drops in each of the first stages are 
about 2 or 3 B.t.u., whereas in the last stages drops of about 
10 B.t.u. may be used. 

(h) One arrangement of the Westinghouse-Parsons turbine is 
shown in section in Fig. 263. After passing the governor valve 
the steam enters at A and flows between the blades on three cyl- 
inders, Ri, R2, and R3, which progress in diameter, until it reaches 
the exhaust opening X. The three balance pistons, Pi, P2, and P3, 
with equalizing pipes Ei, E-i, and £3, balance the thrust, and the 
thrust bearing T constrains the rotor 'to its proper position. 
The governor moves the pilot valve, which in turn controls the 
governor valve. The operation is such as to cause the latter 
valve to constantly move up and down, admitting the steam 
" by puffs," which vary in duration with the load. If the 
demand on the turbine becomes more than can be met by all 
the steam that can flow between the first blades, the turbine's 
speed will decrease slightly and the governor will then open the 
overload valve, thus admitting steam to a point (C) where the 
passage area between blades is greater, so more steam can be used 
to meet the emergency, although less efficiently than before. 




Fig. 264. 

(i) Fig. 264 shows the general arrangement of the Allis- 
Chalmers-Parsons turbine, which is of the same general type as 



390 HEAT-POWER ENGINEERING 

the Westinghouse, but differs somewhat in its arrangement, 
construction, and method of governing. The largest balance 
piston Ps is placed at the exhaust end of the rotor and the gov- 
erning is by the throttling method. 

(j) In multistage turbines the elements in the different stages 
need not all be of the same type. It is sometimes desirable to 
use in the first stages that type which operates best with steam 
at high pressures, and in the remaining stages the type best 
suited for low-pressure conditions. 

189. Applications of the Steam Turbine. Owing to the high 
rotative speeds and to the inability to vary these speeds sud- 
denly or to reverse the direction of rotation, there are many 
fields of " direct driving " which the steam turbine cannot 
enter. 

(a) Driving electric generators, which furnish current for 
almost an unlimited number of purposes, is the largest field of 
application. 

(b) Turbines are used with direct-driven centrifugal pumps 
which discharge against low or high heads (circulating pumps, 
boiler-feed pumps, etc.). 

(c) They are used for driving centrifugal air compressors 
(which are usually multistage), fans, blowers, etc. 

(d) In some instances small low-speed turbines have been 
used for belt driving. Ordinarily it is not feasible to reduce the 
rotative speeds by use of gearing unless specially designed and 
constructed for the purpose. 

(e) The torque on a turbine shaft is relatively very small, 
hence turbines are not applicable where a large starting effort is 
involved. 

(f) In many instances steam is available at pressures which 
are too low to use in an engine, but can be used advanta- 
geously in "low-pressure" or "exhaust-steam" turbines, pro- 
vided a high vacuum can be maintained in the condenser. 

In plants in which engines are operated noncondensing, there 
can be added turbines of this type to receive exhaust steam at 
about atmospheric pressure and to exhaust into a condenser 
having good vacuum. In such cases it is desirable to maintain 
a pressure slightly above atmospheric in the pipes between the 
engine and the turbine to avoid leakage of air into the steam 



STEAM TURBINES 39 1 

with resultant decrease of vacuum. When the steam is received 
at about atmospheric pressure, the exhaust turbine will develop 
a horse power with about 30 pounds of steam per hour, provided 
the vacuum is good. The probable water rate in any case can 
be computed by using Eq. (318). With this and the available 
amount of steam known, the power that can be developed by 
the exhaust turbine can be readily computed. 

Condensing engines can be operated noncondensing with late 
cut-off, thus giving about their normal power, and the exhaust 
steam can be used in a low-pressure turbine, the combined 
outfit thus giving power greatly in excess of (sometimes double) 
the normal power of the engine alone. Such arrangements 
usually are more economical than either the engine under the 
original conditions or a turbine which receives steam direct 
from the boiler. The less economical the engine, the more 
heat remains in its exhaust steam for use in the turbine. 

(g) If the supply of steam furnished a low-pressure turbine is 
intermittent, as in a rolling mill, a regenerator or accumulator 
can be used to make up any temporary deficiency which may 
occur. This device consists of a closed vessel which contains 
water over or through which the steam passes on its way to the 
turbine. Thus this water becomes heated to the temperature 
of the steam. Should the supply of steam cease, the steam 
pressure would decrease and as a result some of the water would 
vaporize and supply the turbine with working substance at 
continually decreasing pressure for a short interval of time. 
Usually there is also provision for supplying steam direct from 
the boilers, through a reducing valve, in case the normal supply 
fails for a considerable length of time; and sometimes the tur- 
bine has a high-pressure stage which is normally inoperative, 
but which is brought into action in such an emergency. 

(h) Marine propulsion is another large field for the appli- 
cation of the steam turbine. A saving in the weight of the 
turbine and of space occupied can be effected by using high ro- 
tative speeds, and the economy can be improved by using high 
bucket velocities. On the other hand, the propeller on a slow- 
moving vessel is inefficient if operated at rotative speeds which 
are high. Hence in applying the turbine to the direct driving of a 
propeller, a compromise must be effected ; evidently the best results 
should be obtained on high-speed vessels, and such is the case. 



392 HEAT-POWER ENGINEERING 

There have been invented numerous speed-reducing devices 
(mechanical, hydrauhc, and electric) to be placed between the 
turbine and propeller shaft, but there is still doubt as to their 
feasibility, and until such devices are used the application of the 
turbine will probably be limited principally to vessels of high speed. 

Special provision must be made for backing; usually a small 
" backing element " is placed at the end of the turbine. As 
turbines are very uneconomical when operating below their 
normal speeds, they should not be used for low-speed cruising. 
Sometimes smaller " cruising turbines " are added for such ser- 
vice. Turbines are not satisfactory when much maneuvering 
must be done, and in some instances a combination of engines 
and turbines has been used for such service, 

190. Advantages and Disadvantages of the Steam Turbine. 

(a) When operating under normal load (i.e., with the usual allow- 
ance for overloading), a comparison of the best performances 
does not show that the turbine has any advantage over the 
engine even when unusually good vacuums are used with the 
former. It is probable, however, that the average large con- 
densing turbine with high vacuum gives better performance 
than the average large condensing engine. In general, non- 
condensing and small turbines do not compare so favorably. 
In many cases it is found that from the standpoint of fuel 
economy there is little choice between the turbine and the 
engine, in which cases the selection must be based on other 
considerations. 

Comparison should be made at normal load and should be either 
on the basis of B.t.u. actually supplied per d.h. p. -minute, or of 
the thermal efficiencies, rather than on the basis of the steam 
used, unless the conditions of operation are identical. 

(b) The water-rate curve for the turbine is usually flatter than 
that of the engine, and hence with widely fluctuating load the 
average economy is nearer the best for that machine; espe- 
cially is this the case if the unit is overloaded. 

(c) The space occupied by the turbine is much less than by 
the ordinary engine, especially if the latter is horizontal. In 
some cases, however, this is partly offset by the greater space 
that may be occupied by the larger size of auxiliary apparatus 
frequently used with turbines. 



STEAM TURBINES 



393 



(d) The turbines use no oil internally, hence the condensate 
is suitable for direct return to the boilers, and the heat-trans- 
mitting surfaces of the boilers, condensers, feed-water heaters, 
etc, being free from oily coating, operate under best conditions. 

(e) Turbines have the advantage of greater uniformity of 
rotation, and can give close speed regulation. If properly " bal- 
anced," they are practically free from vibration, hence do not 
require massive foundations or flywheels. 

(f) Other considerations are the first cost of turbine and gen- 
erator (which is generally less than that of the engine-generator 
outfit) , and the cost of auxiliary apparatus (which is often greater 
with high vacuums). The cost of ground occupied, the build- 
ing and foundations, the reliability, the cost of condensing 
water, supplies, attendance and repairs, the allowance for de- 
preciation, etc., must also be considered. Such matters, how- 
ever, relate to the Economics of Power-Plant Engineering, which 
will not be discussed here. 

(g) There are many fields in which it is necessary to operate 
at low angular velocity, at variable speed, with reversal of motion, 
or with large starting torque, which the steam turbine cannot 
enter. There are other fields in which high angular velocity 
is desirable, or not disad- 
vantageous, and in many 
of these the turbine is as 
satisfactory as, or more so 
than, the engine. 

191. Steam-Turbine 
Performance, (a) Fig. 237 
shows the general character 
of the steam-consumption 
curves for steam turbines, 
the curve for total con- 
sumption being substan- 
tially straight. The water- 
rate curve is usually flatter 
than that of the steam 
engine, which indicates less variation in economy with fluctua- 
tions of load. Inspection of this curve shows that the best econ- 
omy is obtained at the maximum load (not at the normal), — 



\ 








STEAM CONSUMPTION WHEN 
INITIAL PRESSURE ^165 LBS.ABS. 


\ 








SUPERHEAT =0°F. 
VACUUM =28 INCHES 




\ 


^ 


'^Pep 


<.\v. 






































■ 










































V 
























^ 


earn 


err) 


h.p.-h 


1.. 























































i i 






3 


? 




> 1 



Thousand K.W. Rated Power 
Fig. 265. 



394 



HEAT'POWER ENGINEERING 













B.T.U. SUPPLIED 
INITIAL PRESS.= 165 LBS.ABS 
SUPERHEAT= 0° F. 
VACUUM = 28 INCHES 




\ 


^ 


-^ 


^ 


u.pe 


rK.-V 


-.-Mil 








20 

19 

SI 


\ 








> T 


KAD 


,., 









-s 


^ 




jV^tv 




■n:^ 










/' 


B.t. 


1. per 


D.h.i 


.-Min 








is' 

17 
Ifi 


/ 

/ 
/ 


/ 







































12 3 45678 

Thousand K.W..Kated Power 



Fig. 266. 



unless there is an " overload valve " which reduces the efficiency 
when open. 

(b) The curves in Fig. 265 show the economies of the larger 

sizes of standard American 
4ooi \ \ \ iB-T.u. SUPPLIED I turbines when operating 

under rated loads which are 
used as abscissas. 

These curves are based 
on Prof. J. A. Moyer's 
tables,* in which the steam 
consumptions as obtained 
by test are reduced to the 
equivalent values which the 
same turbines would prob- 
ably give if operated under 
pressure of 165 pounds ab- 
solute, zero superheat, and 
28-inch vacuum. The cor- 
rections were made by using the following reduction factors : 

For all types of turbine: 

Per pound of initial pressure, jV per cent. 

Generator efficiency, 91 per cent (300 to 400 kilowatts), 95 
per cent (500 kilowatts), 96.5 per cent (looo to 3000 kilo- 
watts), and 98 per cent (5000 to 10,000 kilowatts). 

For Parsons type: 

Per degree of superheat, xV per cent (300 to 1000 kilowatts) 

and \ per cent (1200 to 7500 kilowatts). 
Per inch of vacuum, 4 per cent (300 to 1000 kilowatts) and 

3 per cent (1200 to 7500 kilowatts). 

For Curtis type (may also be used for Rateau and Zoelly turbines) : 
Per degree of superheat, ^ per cent. 

Per inch of vacuum, 7 per cent (26 to 28 inches) and 9 per 
cent (28 to 29.5 inches). 

These correction factors should be used only when the changes 
involved are slight, otherwise the results may not be reliable. 

(c) In Fig. 265, the curve for " steam per d.h.p.-hr," is based 
on the brake horse power, or power delivered by the turbine 



* Page 287, Moyer's "The Steam Turbine." Wiley & Sons. 



STEAM TURBINES 



395 



shaft, and does not include the generator losses. The other 
curve includes the losses of both the turbine and the generator. 

(d) Fig. 266 shows the B.t.u. consumptions and the thermal 
efhciencies corresponding to the water-rate curves of Fig. 265. 
Values better than here shown can be obtained by using higher 
superheats, higher pressures, and lower vacuums — especially 
by using the latter. 

Some of the best results so far obtained with large turbines, 
are given in Table X below. 1 



TABLE X. — STEAM-TURBINE PERFORMANCE. 



10186 
8563 
6257 



Gauge 
Pressure. 
Lbs. sq. in. 



176 
168 
189 



Super- 
heat. 
°F. 



147 

59 

176 



Back Pres- 
sure. 

Lbs. sq. in. 
abs. 



0.26 

G.9 

0.44 



Pounds 
Steam per 
EL h.p.-hr. 



9.62 
10.77 



B.t.u. per 

EL h.p.- 

min. 



200. 

187.3 

185.7 



Thermal 
Efficiency 
(Elect.)." 



21 . 2 

22.65 

22.83 



Over- 
all 
Efficien- 
cy.§ 



61 .9 

68. 

69.4 



* Proc. Nat. El. Lt. Assoc, June 4, 1907. § Including Generator. 

t Page 2089, Journal A.S.M.E., Dec, 1910. 

t (London) Engineering, March 10, 1911, or page 748, Power, April, 1911. 

(e) Small turbines are generally much less economical in the 
consumption of steam than large ones. In most instances this 
is largely due to the use of 



^30 













A 




STEAM PRESS. 150 LBS. GAUGE 
DRY STEAM 
ATMOS. EXHAUST 


-B 
C 
C 
D 




^^^^^ 














E 


^^^ 


^^ 


50 




E 




200 










F 

Lo 


ai 





bucket velocities which are 
much less than those cor- 
responding to the best per- 
formance, and which result 
from using small wheel di- 
ameters and low rotative 
speeds which permit of di- 
rect connection to genera- 
tors, pumps, etc. The 
economy of such turbines 
is greatly influenced by a 
change in bucket speed. 

Fig. 267 shows curves of 
steam consumption per brake horse-power for several types of 

1 Also see Christie, " Present State of Development of Large Steam Turbines," 
Trans. A.S.M.E., 1912. 



^^ Load 
Fig. 267. 



m 



396 HEAT-POWER ENGINEERING 

small turbines.* It shows that in general the smaller sizes have 
poorer economy. 

(f) The results of some tests of the 59th Street Power Plant 
of the Interborough Rapid Transit Co., New York City,t can 
be used to compare the performances of the same power plant 
operating first without and then with exhaust steam turbines. 
This plant was originally equipped with condensing engine-gen- 
erator units each developing 5000 kw. at normal (economical) 
load, and having a maximum rating of 7500 kw. Subsequently, 
exhaust steam turbines of 7500 kw. maximum capacity were 
added, and these were arranged to operate with high vacuums 
on steam received at about atmospheric pressure from the 
engines, which latter were changed to have later cut-offs than 
before. The addition of the turbine to one of the engine units 
gave the following results: — 

(i) The maximum capacity was doubled. 

(2) The load giving the best steam performance (or load 
under which the unit should normally operate) was increased to 
about 2| times its former value. 

(3) The average steam economy (between 7000 and 15,000 
kw.) was 25 per cent better than that of the old engine unit. 

(4) It was estimated that the average steam economy was 
13 per cent better than would have resulted by using a high- 
pressure turbine of the best design in place of the combined unit. 

(5) The average thermal efficiency of the combined unit was 
20.6 per cent (between 6500 and 15,500 kw.). 

* See Orrok, "Small Steam Turbines," Trans. A. S. M. E., 1909. 
t Trans. A. S. M. E., 1910, page 78. 



CHAPTER XXIIL 

EXTERNAL-COMBUSTION GAS ENGINES. 

192. Definition, (a) The name gas engine is applied to 
prime movers in which the working substance is material in 
gaseous form comparatively far removed from the conditions of 
liquefaction. Hence the working substances may be assumed to 
obey the laws of ideal gases, and each gas engine follows approxi- 
mately one of the gas cycles discussed in Chapter VIII. 

(b) At present gaseous working substances consist of air mixed 
with other materials such as carbon monoxide, hydrocarbon 
vapors and gases, water vapor, and carbon dioxide. 

(c) The " hot body " is approximated in real engines by the 
burning of fuel in some chamber at a rate which maintains the 
required high temperature. In some types of gas engines the 
fuel, and resulting hot "products of combustion," are separated 
from the working substance by metallic walls through which 
the heat received by the working substance must pass. Such 
engines are known as external-combustion gas engines. 

In other gas engines the fuel and the air for its combustion 
are burned inside the cylinder of the engine, and the hot products 
of combustion form the expanding working substance. Such 
engines are called internal-combustion gas engines, or simply 
internal-combustion engines. 

193. The Hot-Air Engine, (a) Many attempts have been 
made to utilize air as a working medium in external-combustion 
engines, but only two such engines survive to-day in this country, 
and they are built only in small sizes and for special service. 
Inventors have long tried to produce an actual gas engine to 
work with close approximation to the Carnot cycle. Even if 
this were possible, it would be unwise commercially because of 
the excessive cylinder volume necessary for a given output of 
power. 

This may be made clear by drawing, as in Fig. 268, a Carnot 
cycle, an Ericsson cycle, and a Stirling cycle for comparable 

397 



398 



HEAT-POWER ENGINEERING 



conditions so as to show the greatest volume occupied by the 
gas in each case. This is best done by imagining one pound of 
gas (air in the figure) to receive the same amount of heat and to 
work between the same temperature limits in each case. The 
efficiency and work done will then be the same in each case, and 
will be 

Ef^(Ti- T2)/Ti, 
and 

AE = AQx XEf= Aft (Ti - T2)/T^. 
The figure shows that the maximum volume occupied by the 
working substance, and hence the necessary cylinder volume, is 

much greater in the case of the 
Carnot engine than for either of 
the others. 

(b) The cylinder volume, how- 
ever, determines to a consider- 
able extent the size and cost of the 
engine. As will be brought out 
later, the real external-combus- 
tion gas engines operating on the 
Stirling and Ericsson cycles are 
almost prohibitively large, and 
it is therefore obvious that the 
Carnot gas engine with external 
combustion must be commer- 
cially impossible. 

(c) The two external-combus- 
tion gas engines now in use in 
this country are the Rider hot- 
air engine and the Ericsson 
hot-air engine. The former 
approximates the Stirling cycle 
and the latter the Ericsson cycle. 

Both of these engines are direct-connected to small water pumps 
which utilize the net work of the engine. They are simple and sat- 
isfactory pumping engines,particularly for farm and suburban use. 
(d) The capacity, that is, the power made available, is limited 
by the slow rate of heat transfer between the metallic walls and 
the more or less quiescent gas ; by the slow rate of heat conduction 
in the gas itself; by the low specific heat and density of the gas; 




10 20 

volume, Cu.Ft. 

Fig. 268. 



EXTERNAL-COMBUSTION GAS ENGINES 



399 



and by the comparatively low maximum temperature at which 
it is advisable to maintain metal. 

In order that gas may absorb or give up heat rapidly, it must 
pass over the metallic surfaces in a thin stream and at high 
velocity. This necessitates a large engine. The time neces- 
sary for heat exchanges is so great that the engine must run at 
very slow speeds with few cycles per minute. Obviously, the 
smaller the number of cycles the greater must be the energy 
made available per cycle, and hence the greater the size of the 
engine to deliver a given amount of power. 

The effect of low specific heat is to increase the weight of gas 
necessary for a given heat change, and the low density results 
in a large volume for a given weight. Both effects increase the 
size and cost of engine for a given power. 



194. Rider Hot-Air Engine, (a) This engine, which approxi- 
mates the Stirling cycle (Section 54), is shown in Fig. 269, and by 
comparing it with Fig. 23, re- 
produced at {h) in the upper 
right-hand corner of Fig. 269, 
it is seen to have all the parts 
of the ideal engine following 
this cycle. In the two figures 
similar parts are designated 
by the same letter. The ideal 
hot body is replaced by a fur- 
nace, the gases of which at 
temperature Ti jacket the hot 
cylinder Y. The regenerator 
R is approximated by a pass- 
age filled with closely spaced 
plates HH. The cold cylin- 
der Yi is jacketed by water X 
from pump P and is main- 
tained at a practically con- 
stant temperature T2. The 
water replaces the cold body. 
By means of connecting rods 
/ and /' the pistons D and C are connected to cranks / and /' 
which are fastened to the shaft, with the crank for the hot cylinder 




REAL ENGINE 
Fig. 269. 



400 HEAT-POWER ENGINEERING 

leading the other * by about 90 degrees. The crank shaft carries 
a flywheel W which maintains uniformity of rotation, even 
though the power, developed and delivered, varies widely. 

(b) In the ideal cycle. Fig. 22, and (a) in Fig. 269, it is 
assumed that during the isothermal reception of heat by the gas, 
the left piston remains stationary at the bottom of its stroke, 
while the right piston rises; that during the isothermal rejection 
of heat the reverse action occurs ; and that during the isovolumic 
changes the two pistons move at such rates as to keep the total 
inclosed volume constant while the gas passes through the 
regenerator. 

In the actual case these actions are roughly approximated by 
connecting the pistons to cranks which are nearly at right angles. 
When either piston is at or near its lowest position, most of the 
working substance is in the other cylinder, where the piston is 
at about half-stroke (since the cranks are at about right angles). 
The material meanwhile is undergoing an isothermal change, 
which is expansion if the gas is in cylinder Y, or compression if 
in Fi. In two intermediate positions of the cranks the pistons 
are moving with equal and opposite velocities, while the gas 
is undergoing isovolumic transfer from one cylinder to the other. 
Thus in the Rider engine the Stirling cycle is roughly approxi- 
mated, with considerable blending between the various processes. 

(c) The actual diagram obtained from this engine cannot readily 
be directly compared with the theoretical, and a reproduction 
is therefore omitted. The maximum and minimum temperatures 
are respectively lower and higher than the theoretical, and the 
corners of the diagram are very much rounded. 

(d) If the furnace temperature be assumed at 1500° F., a low 
value, and the jacket temperature at 60°, a rather high value, 
the Stirling cycle efficiency is 

The actual thermal efficiency on the i.h.p. (TIEf) is seldom 
as much as 2 per cent, so that the best indicated efficiency is 
about 

LEf = 2/73.5 = 0.027 = 2.7 per cent. 

* That is, preceding it in the direction of rotation. 



EXTERNAL-COMBUSTION GAS ENGINES 



401 



The corresponding efficiency for internal combustion gas-en- 
gines and steam engines is generally 50 per cent or more. The 
poor economy of this engine is thus very striking. 

195. Ericsson Hot-Air Engine, (a) This engine, which ap- 
proximates roughly the Ericsson cycle (Section 55), is shown in 
Fig. 270, in which the parts are lettered to correspond with the 




REAL ENGINE 

Fig. 270. 

theoretical engine shown in Fig. 23. The furnace U replaces 
the hot body; below the " displacer " piston j is the hot cylinder 
Y, jacketed by the furnace gases, and above it is the cold cylin- 
der Fi with jacket X supplied with water from pump P. The 
upper or working piston 2 transmits the power. When the 
displacer piston j is up, most of the gas is below it in the hot 
cylinder. Upon descending, this piston transfers the gas to the 
cold cylinder Y\ above, and when ascending, returns it to the 
hot cylinder Y. The function of the regenerator R is performed 
by the walls of the cylinder and of the loose-fitting displacer 
piston, between which the gas passes in transferring from one 
cylinder to the other. 

The engine has an ingeniously arranged mechanism which 
gives such kinematic motion to the displacer and working pistons 



402 HEAT-POWER ENGINEERING 

as to produce approximately the PV-changes of the theoretical 
Ericsson cycle. 

(b) The conditions of heat transfer are even poorer in this 
engine than they are in the Rider, and as a result the power 
developed for the same heat supply, and for same size of cylinder, 
is only about one-third of that obtained with the other engine. 

(c) It is worthy of note that a very large hot-air engine of a 
different type, which was constructed by Ericsson, gave a thermal 
efficiency of about lo per cent. It was, however, enormously 
bulky and mechanically unsatisfactory. 



CHAPTER XXIV. 

INTERNAL-COMBUSTION ENGINES. 

Methods of Operation. 

196. Advantages and Types, (a) Although external-combus- 
tion engines with gaseous working substance are not generally 
commercially successful, the internal-combustion engine, on the 
other hand, is widely used, and is capable of giving the highest 
economies now attained by any type of heat engine. 

The success of the internal-combustion engine is chiefly due 
to the fact that, since the products of combustion constitute the 
working substance, the maximum temperature is tha't due to 
combustion; whereas in the external-combustion engine the 
maximum temperature of the working substance is limited by 
the capacity of metallic walls to withstand high temperature, and 
to transmit heat. 

In internal-combustion engines with proper design the highest 
temperature attainable may be used without danger to metallic 
walls, and it is thus possible to approach theoretical efficiencies 
corresponding to temperatures of from 2500° to 3000° F. Be- 
cause of the high pressures that accompany high temperatures, the 
engines are also small for a given capacity. 

(b) During the past twenty years the use of internal-com- 
bustion engines has rapidly increased, until now many large 
power plants depend entirely upon them for power. These 
engines operate on either the Otto cycle or the Diesel cycle. 
Engines following the latter cycle were uiitil recently a more or 
less special type adapted only to certain limited conditions, but 
this limitation is rapidly disappearing. 

(c) There are two distinct types of engine following the 
Otto cycle; one requires two piston strokes, and the other four, 
to complete a cycle. They are known as two-stroke cycle 
and four-stroke cycle engines, or improperly as " two-cycle " 
and " four-cycle " engines. The four-stroke cycle is in more 

403 



404 



HEAT-POWER ENGINEERING 




To Atmosphere 



Fig. 271. 



common use, though it has several theoretical and practical disad- 
vantages as compared with the other type. 

197. Cylinder Operations of Four-Stroke Otto Cycle, (a) 

The heat is evolved within the cylinder by the burning of a 

mixture of fuel gas, or vapor, 
with air, which supplies oxygen 
for combustion. The gaseous 
products of combustion form 
the working substance, which, 
after expansion, must be ex- 
pelled from the cylinder to 
ai-^ give place to a fresh combusti- 
ble charge for the next cycle. 
The engine is shown diagram- 
matically in Fig. 271. 
(b) Imagine a cylinder as shown in the figure, with an inlet 
valve / and an exhaust valve E located in the head and arranged 
to open inwardly; and assume that the piston is in its extreme 
left position, that its motion can be controlled as desired, that a 
cycle has just been completed, 
and that the " clearance space'' 
or ^^ combustion space'' between 
the face of the piston and the 
cylinder head is filled with burnt 
gases at atmospheric pressure. 

Now with the valve E closed, 
and with / open to a supply of 
combustible mixture at atmos- 
pheric pressure, the first stroke 
of the piston (to the right) will 
cause some of this mixture to pass 
into the cylinder, where it will mix with the burnt gases, and thus 
diluted will fill the available space at approximately atmospheric 
pressure. The line ed in Fig. 272, at a height of 14.7 pounds 
per square inch above the horizontal axis, represents this process. 
Now imagine the inlet valve / closed and the piston moved to 
the left performing the second stroke. During this stroke the 
mixture will be compressed until, finally, its volume is reduced 
to that of the clearance space. This compression may be 



h- 












\ 










\ 


V 






a 


^^ 






3^ 



V 
Fig. 272. 



INTERNAL-COMBUSTION ENGINES 405 

assumed to be adiabatic, although this would not be absolutely 
true in any real case on account of the thermal properties of the 
metallic walls. The ideal process is represented by the adiabatic 
compression line da, corresponding to'the similar line in Fig. 26, 
page 94. 

At this point a the charge is ignited by an electric spark, or 
other means, and it may be assumed to burn completely with 
the piston stationary. This would cause an increase in tem- 
perature and pressure corresponding to the ideal isovolumic 
addition of heat, as shown by the line ab, Fig. 272. 

The piston will then make a third stroke, being driven out 
by the high-pressure gas expanding according to the curve he, 
which may be considered an adiabatic. 

In the ideal case heat would be given to the cold body accord- 
ing to process cd, while the volume remained constant, but in 
the actual case the exhaust valve E, in Fig. 271, is opened, 
allowing the high-pressure gas to expand into the atmosphere 
until the pressure in the cylinder falls to d. 

During the fourth stroke the returning piston expells the remain- 
ing gas according to the line de, and at e the starting conditions 
are restored, with the clearance space filled with burnt gases at 
atmospheric pressure. 

(c) Although four strokes are required to complete the prac- 
tical cycle, the work area under the line ed cancels that under de; 
thus the ultimate result is the development of a cycle inclosing 
the work area ahcda, exactly as in the ideal Otto engine discussed 
in Section 56, page 94. 

The two strokes corresponding to ed and de are really pumping 
strokes, used to draw in the new charge of combustible and to 
expel the burnt gases. They are, therefore, necessitated by prac- 
tical considerations, though not essential to the ideal cycle. 

(d) A real engine of this type is shown semi-diagrammatically 
in Fig. 273. The cylinder head has been broken away to show 
the valves, which correspond exactly to valves / and E of Fig. 271. 
Instead of using a mixture reservoir, assumed in the ideal case, 
the real engine forms its own mixture during the suction stroke, 
drawing the constituents through the pipes in the figure. 

The cylinder and cylinder head of the real engine are water- 
jacketed to prevent overheating of the metal. 

The valves in this case are positively operated by linkage 



4o6 



HEAT-POWER ENGINEERING 



(not shown) moved by cams on the " half-time shaft," or " cam 
shaft," shown along the side of the engine. This shaft is driven 
by gears from the crank shaft, the gears being so proportioned 
as to give the cam shaft one revolution for every two revolutions 
of the crank shaft. 




Fig. 273. 
198. The Air Card, (a) The series of operations just described 
cannot be carried out perfectly in any real engine; thus the 
picture of what actually occurs in the working cylinder is quite 
different from Fig. 272. 

(b) The losses in the cylinder are commonly determined by 
comparing the actual diagram with the diagram of an ideal Otto 
cycle with air as the working substance. This ideal diagram is 
also called the " air card," or " air diagram," and it is constructed 
for an engine like that shown in Fig. 271, operating as described 
in the last section, but with air only in the cylinder. 

Referring to Fig. 272, it is assumed that at the point d the 
clearance and displacement volumes are filled with air at atmos- 
pheric pressure and temperature; that the compression da is 
adiabatic; that at a heat is added equal to that which would be 
liberated by complete burning of the combustible mixture used 
per cycle in the real engine; that from b the expansion is adia- 
batic to c; and that the heat is then removed, as in the ideal 
case, until the air returns to starting conditions at d. 

(c) The pressure at a can be found from Eq. (45 b) and the 
temperature can then be computed from Eqs. (51) and (52). 



INTERNA L-COMB USTION ENGINES 



407 



The height of the point b is obtained thus: First find the theo- 
retical temperature to which this quantity of heat would raise the 
charge of air, with heating taking place at constant volume, and 
with specific heat of air constant; then determine the corre- 
sponding pressure Pt from the relation " = — ^ • 




199. Real Indicator Card for Four-Stroke Cycle, (a) In 

Fig. 273 is shown a real engine with the cylinder surrounded 
by a water jacket to prevent overheating of 
the metallic walls. Fig. 274 shows another 
engine in which the cylinder is covered by 
ribs presenting large radiating surface so 
that air may be the cooling medium instead 
of water. The actual cards obtained from 
such engines dififer in many respects from 
the ideal air card just discussed, because 
of (i) chemical and physical properties of 
the real working substances; (2) thermal 
properties of the metallic parts of the en- 
gine; and (3) mechanical faults, such as 
leaking piston and valves. The variations 
are shown in Fig. 275, in which the real 

card (full lines) has been superimposed on the ideal diagram 
(dotted). Parts of the real card have here been overdrawn to 
accentuate the variations. 

(b) Starting at the end c of the expansion line, in the ideal 
case with the mechanism of Fig. 271, the exhaust valve would 
be opened to allow the charge of the preceding cycle to escape 
into the exhaust pipe. In the real case, however, this valve must 
start to open before the end of the stroke, say at c' , which is 
usually at from 85 to 90 per cent of the out-stroke. This is neces- 
sary so that the valve, which cannot be opened instantly to its 
full extent, may have time to open fully before the end of the 
stroke is reached; and because the gas in the cylinder, due to 
its inertia, takes an appreciable time to pass through the exhaust 
valve despite the fact that the gas pressure of from 15 to 35 pounds 
or more above the atmosphere is available to accelerate it. 

From c' the expansion line drops rapidly to the end of the 
stroke, both because additional space is vacated by the piston 



4o8 



HEAT-POWER ENGINEERING 



as it continues outward, and because of the exit of gas from the 
cyhnder. 

(c) The Hne d'e' is higher than the ideal exhaust hne de. 
This is due to the pressure difference necessary to cause the flow 
of gas through the exhaust valve and pipe to the atmosphere. 
As the area opened by the valve is limited by practical consider- 
ations, a high average velocity of gas flow through this valve is 



P400 



1 ' 




600 






















1 


\ 


400 
P 




ACTUJAL DIA 


3RAM 




1 






\ 








1 

1 


\ 


200 





\ 








f^ 


^ 

:==:- 


^-^ 




3 


1 \ 


X \ 


.0-2 -04 .06 .08 .1 


\ 












^^ 


> 


^ 


^^^^^ii: 


l"r7' 




e^ 










— 6^d 










—f- 






~°9 





V 
Fig. 275. 



necessary in order to empty the cylinder in the available time. 
This velocity varies from 80 to 125 feet or more per second, and 
to produce it the exhaust pressure line d'e' must be from one to 
three pounds above atmospheric. Instead of being straight, 
this line is generally more or less wavy because of the inertia of 
the gases. 

(d) At e', with the piston at the end of the stroke, the clear- 
ance is filled with products of combustion at a pressure slightly 
above atmospheric and at a temperature probably 700° to 900° 
Fahr. As the piston starts on the " suction stroke," these 
gases expand to some pressure /, from one to six pounds below 
that of the mixture supply (which is usually at atmospheric 
pressure) , before the new charge begins to flow through the open 
inlet valve into the cylinder. This flow continues as the piston 
moves out until the end of the stroke is reached at g, when the 
cylinder is filled with a mixture of the new charge and the 



INTERNAL-COMBUSTION ENGINES 409 

burnt gas previously left in the clearance. This " suction line,'' 
fg, is only approximately straight and horizontal. 

Evidently during both the exhaust and the suction strokes the 
piston must do work on the gas, and this decreases the power that 
the engine can deliver. 

(e) The compression line ga' \s generally below da (i) because 
compression begins at g with pressure below atmospheric; (2) 
because the physical properties (7, etc.) of the real mixture are 
different from those assumed for air (3) because the process is 
not adiabatic, for there is heat interchange between the gas and 
the walls of the piston, cylinder, and head; and (4) because of 
leakage past piston and valves. This process is generally inter- 
mediate between an adiabatic and an isothermal. 

(f) At or near a' ignition occurs, and as it actually takes an 
appreciable time for the flame to spread throughout the mixture, 
and as the piston does not remain stationary at the end of the 
stroke during the complete process of combustion, the sloping 
ignition line a'b' results, instead of the vertical line ah of the 
ideal process. Combustion is seldom complete, even when the 
highest pressure is reached, hence heat is still being added when 
expansion starts. 

(g) The pressure does not rise as high as the ideal value b, 
presumably because (i) the initial pressure a' is less than the 
ideal at a; (2) the movement of the piston increases the volume 
during combustion ; (3) the average specific heat of the mixture 
is different from that assumed for air and increases as the tem- 
perature rises; (4) the surrounding metallic walls absorb some 
of the heat generated; (5) the chemical reactions accompanying 
combustion may result in products occupying less volume than 
the original mixture; (6) there may be a certain amount of dis- 
sociation at the higher temperatures; and (7) there may be 
leakage past the piston and through the valves. 

(h) The expansion line is at first generally above an ideal 
adiabatic curve h'l because of " after burning,'' or the continu- 
ation of combustion, which usually adds heat in excess of that 
absorbed by the metal walls and that converted into external 
work. Later, as the motion of the piston continues, the relatively 
cooler cylinder walls are uncovered and they rapidly absorb heat 
from the gas, causing the expansion line to drop below the adia- 
batic. 



4IO HEAT-POWER ENGINEERING 

(i) During part of the compression, and all of the combustion 
and expansion, heat is absorbed by the inclosing metallic walls, 
from which part of it is carried away by the water or air jacket. 
This is a direct loss, but it is necessary in order to prevent over- 
heating the metal. 

(j) During the suction stroke the incoming gas receives heat 
from the confining walls and from the exhaust gas still remain-- 
ing in the clearance space, until at the end of the stroke the gas 
and inner surface of the walls are probably at nearly the same 
temperature. Because of the expansion of the gas due to this 
temperature (which is often from 700° to 900° Fahr.), and because 
of the reduction of pressure below atmospheric during the suc- 
tion stroke, the weight of fresh mixture drawn in is reduced, and 
hence less than the theoretical work per cycle is done in a given 
cylinder. 

200. Losses in the Four-Stroke-Cycle Engine, (a) A com- 
plete analysis of all the losses in the cylinder of an internal-com- 
bustion engine would be very complicated, and is as yet unsat- 
isfactory because of the lack of experimental data. For the 
purposes of this book, it will serve to indicate the principal 
sources of loss and to treat them qualitatively rather than quanti- 
tatively. 

(b) The Otto cycle efficiency is from Eq. (81) 

-/— (r' 

It is seen to be dependent only on the compression ratio ( Va'/ Vg), 
which the designer can control, subject to practical considera- 
tions, by the selection of proper clearance volume, Va'- Thus 
theoretically, nothing is lost by the low pressure or high tem- 
perature at g. 

(c) Section 199 (j), however, showed that the actual weight 
of fresh charge drawn into the cylinder during the suction stroke 
is always less than the theoretical, and this of course reduces the 
power developed. 

Let Vs' be the volume corresponding to the actual weight of 
gas drawn in, and Vs be that equivalent to the piston displace- 
ment per stroke, both volumes being measured at atmospheric 

pressure and temperature. Then the ratio (vr"| is called the 



INTERNAL-COMBUSTION ENGINES 411 

volumetric efficiency. In practice its value may reach 90 per 
cent in well-designed slow-speed engines, or it may be reduced 
by high speed or incorrect design to 50 per cent or less. Evi- 
dently, in a given engine the amount of heat liberated per 
cycle depends on the volumetric efficiency, and hence for definite 
power output a lower volumetric efficiency makes necessary larger 
cylinder and greater cost of engine unless operated so as to give 
more cycles per minute. 

(d) The effect of the falling of the real compression line 
below the adiabatic, upon the performance and efficiency of the 
engine, is difficult to state in any general way. Since the line 
lies between the isothermal and adiabatic, the work done is 
slightly less than that which corresponds to an adiabatic process, 
and this compensates more or less fully for the loss of heat which 
makes this line fall below the adiabatic, and for the correspond- 
ing lowering of the efficiency. 

(e) The combustion line a'h' represents the most complicated 
process in the cycle and is the most difficult to investigate, as 
the phenomena take place with comparative rapidity and vary 
with the character of the mixture, the method of ignition, the 
surface form of the combustion space, etc. The real loss during 
this process cannot be accurately measured by comparison with 
the ideal air diagram, but could be determined by comparison 
with a card drawn for the working substance actually used in 
the real engine, considering specific heats variable and accounting 
for any other theoretical modifying conditions. As this would 
mean a different standard for every fuel, and for every different 
mixture of fuel and air, the " air standard " is retained for 
simplicity. 

In considering the sloping combustion line a'h' , it is again a 
case of balancing gains and losses. The piston movement 
reduces the maximum pressure and temperature, thus decreasing 
the heat lost to the cylinder walls, but this is offset more or less 
completely by the larger surfaces exposed while the temperature 
is high. The slope which will give the highest efficiency cannot 
be predicted, but usually an inclination which will bring the top 
of the combustion line at about 2 per cent of the stroke seems to 
give the best results. The loss of area between the real and 
theoretical combustion lines is partly compensated by the broad- 
ening of the top of the diagram. This change in form of the 



412 HEAT-POWER ENGINEERING 

diagram improves the mechanical operation of the engine be- 
cause the pressure changes are less sudden and less intense. 

(f) The expansion line h'c' generally incloses slightly more 
area than the adiabatic h'l (Fig. 275), unless the engine is of 
such proportions as to expose excessive wall area. 

By opening the exhaust valve at c' , as in Fig. 276 (a), less area 
of diagram is usually lost than if the opening is at the end of 



Jl^"' 



Fig. 276. 

the stroke, as, in Fig. 276 (&) ; and as less hot gas remains in the 
cylinder the tendency to overheat the metal walls is reduced. 

The actual heat interchanges during exhaust are problem- 
atical. The enormous rush of gas through the exhaust valve 
consumes heat which is lost to the atmosphere, but there is a 
corresponding gain due to increased volumetric efficiency result- 
ing from contact of the new charge with cooler walls. 

Quite remarkable success has been achieved by engines in 
which cold air is blown through the cylinder during part of the 
exhaust period. This operation cools the walls and tends to 
remove the burnt gases from the clearance space, and hence the 
charge drawn in is cooler and purer than in the ordinary type of 
engine. Such engines are known as "scavenging'' or ''positive 
scavenging " engines. 

201. Requirements for High Efficiency of Combustion^ 

(a) There are two antagonistic requirements for high efficiency 
of combustion: (i) The final compression pressure and temper- 
ature (at a' , Fig. 275) must he high, since this not only gives high 
efficiency theoretically (see Eq. (80)), but also because experience 
shows that the charge is often more readily ignited and burned 
from high pressure. The limit is reached when the pressure is 
so high as to cause " preignition," that is, spontaneous ignition 
of the mixture during compression. With other things equal, 
the greater the pressure and temperature at the end of compres- 
sion, the higher will be the final temperature at b'. (2) The 
maximum temperature attained (at the point h') should he as low 
as possible, because the specific heats and loss of heat to metallic 
walls increase rapidly at high temperatures. 



INTERNAL-COMBUSTION ENGINES 413 

(b) These two requirements for high actual efficiency can be 
barmonized in practice by using a mixture with large excess of 
air. This may be highly compressed without danger of preigni- 
tion; it burns rapidly enough at high pressures for satisfactory 
combustion; and, because of the excess of air present, the final 
temperature attained is comparatively low. 

Unfortunately, however, the mixture which gives highest 
actual efficiency " on the brake " does not give maximum 
possible power from a cylinder of given size operating at given 
speed; thus there is a tendency to operate engines with mixtures 
" richer " in combustible than those giving the highest efficiency. 

202. Indicated Work and Power of the Four-Stroke-Cycle 
Engine, (a) In the diagram shown in Fig. 277, with the " lower 
loop " fghef considerably exaggerated, 
the arrows indicate the directions in 
which the various lines are traced. 

(b) If areas on a PV-diagram sur- 
rounded by lines generated in one di- 
rection (here clockwise) represent work 
done upon the piston, or positive work, ''~. 
then areas inclosed by lines of reverse 
direction (here counter-clockwise) indicate work done hy the 
piston upon the working substance, or negative work. 

Thus the work represented by the upper area or " loop," 
abcdea, is positive; the work corresponding to the " lower loop," 
fghef, is negative; and the net useful work on the piston would 
be represented by the difference between these areas. 

(c) The exact interpretation of " indicated power " in the 
case of a four-stroke-cycle gas engine is still unsettled. All 
things considered, it seems best to calculate i.h.p. from the upper 
loop alone. Then the difference between the i.h.p. and the d.h.p. 
is the work lost in overcoming both the fluid friction and the 
friction of the mechanism. 

The fluid-friction loss is measured by the area of the lower 
loop ; it would equal zero with frictionless flow. The engine-friction 
loss is the difference between the total friction loss and that due 
to fluid friction ; it would equal zero with a frictionless mechanism. 

(d) The mechanical efficiency is the ratio .', '^' - As applied 
to gas engines, it includes both kinds of friction loss when the 




414 



HEAT-POWER ENGINEERING 



i.h.p. is computed according to the method just given. It is 
advisable to adhere to this method because of the difficulty of 
obtaining the correct area of the lower loop. 

203. The Two- Stroke- Cycle Otto Engine, (a) Comparison 
of single-cylinder single-acting Otto engines of the four-stroke- 
cycle and the two-stroke-cycle types shows that in the former 
there is one power stroke out of four, while in the latter there is 
one power stroke out of two. Hence with the same rotative 
speed and cylinder dimensions the two-stroke-cycle engine theo- 
retically should give twice the power of the four-stroke-cycle 
engine, and should require much less flywheel weight to main- 
tain the same degree of uniformity in rotative speed. 

Moreover, in the four-stroke-cycle engine the mechanism, which 
is designed for very high pressures, is used half the time for pump- 
ing gas at low pressure (while forming the lower loop of the 
diagram). And to make matters still worse, the density of the 
mixture, and therefore the weight of gas drawn in per cycle, is 
reduced by heat received from the hot cylinder walls, and this 
increases the cylinder size for a given power output. In the 
two-stroke-cycle engine, on the other hand, a separate, specially 
designed pump, with cool walls, may be used more effectively 
for this service. 

(b) The two-stroke-cycle engine is represented diagrammatic- 
ally in Fig. 278. The pump cylinder has an inlet valve A, and 



rM-4Vr 




Fig. 278. 

a discharge valve /, which latter also serves as an inlet valve 
to the power cylinder. This cylinder has a ring of ports, E, cut 
through the walls at such a point that the piston, by uncovering 
them near the end of its stroke, acts as an exhaust valve. 



(5) 

U.TLbs. sq. in. 



INTERNAL-COMBUSTION ENGINES 415 

(c) Now imagine the ideal cycle performed without mechani- 
cal or thermal loss as follows: Consider the power cylinder 
filled with mixture at atmospheric pressure, the power piston 
just covering the exhaust ports E. The first stroke is to the left, 
causing compression of the charge according to the line d'a in 
Fig. 279 (a). Combustion produces the 
line ab. Expansion during the second 
stroke occurs according to the line he; 
and when the piston passes the ports, E, 
exhaust occurs according to the line cd, 
thus nearly completing the cycle in the 
power cylinder. Meanwhile the pump 
piston has moved down and drawn in 
from the reservoir a charge of mixture 

sufificient to fill the power cylinder, the theoretical process being 
represented by e/ in Fig. 279 {b). The valve A is then closed, 
and after the pressure in the power cylinder has dropped to 
atmospheric at d in Fig. 279 (a), the valve / is opened and the 
pump piston is quickly raised, driving the mixture into the power 
cylinder, according to the theoretical line fe. While this is occur- 
ring the power piston moves from d to d' . 

In the ideal case the charge entering the power cylinder will 
drive the remaining exhaust gases out through the ports as it 
moves down the length of the cylinder in a solid column, and 
arrive at the exhaust ports just as the returning power piston 
covers them. The power cylinder is thus charged with a com- 
bustible mixture, with volume as shown at d' , at atmospheric 
pressure, and with the conditions assumed at starting. 

The theoretical pumping work, represented by the area under 
ef minus the area under fe, is zero, as in the case of the ideal 
four-stroke cycle. In the power cylinder the Otto cycle is 
followed except at the end cdd' , which is modified for practical 
reasons. 

(d) The differences between the actual- work diagram and 
the ideal Otto cycle are quite similar to those occurring in the 
four-stroke-cycle engine, and arise largely from the same causes. 

The pump does not actually operate in the ideal manner. It 
is usually driven from a crank on the engine shaft, and in con- 
sequence the gas must be pumped to some intermediate reservoir, 
where it must be maintained at a pressure of from 0.5 to 7 pounds 



4i6 



HEAT-POWER ENGINEERING 



above atmospheric in order to fill the power cylinder in the 
short time available after the inlet valve opens. Energy is not 
only lost in overcoming the pump friction and resistance to flow, 
but is also expended in compressing the mixture in the pump 
cylinder. The work done on the gas is shown by the area of 
the actual pump card. 

Because of its great velocity, the entering charge generally 
mixes more or less with the burnt gases, and some portion usu- 
ally escapes through the exhaust ports before they are covered. 

Although theoretically the two-stroke-cycle engine would 
develop twice the power given by a four-stroke-cycle engine of 
the same size and r.p.m., the actual ratio is usually from 1.4 to 
1.6, owing to the losses due to the method of operation. 




Fig. 280. 



(e) In some two-stroke-cycle engines the power cylinder is 
first scavenged by admitting air under pressure ahead of the 
mixture so that none of the fresh charge escapes with the ex- 
haust. The saving thus effected is, however, offset more or less 
completely by the necessity of using two pumps instead of one, 
with increased complexity and greater expenditure of energy 
in pumping. One engine of this type is shown semi-diagram- 
matically in Fig. 280 and is known as the Koerting design. 

In some single-acting engines operating on the two-stroke 
cycle, the mixture is first admitted to the crank case, as in 



INTERNAL-COMBUSTION ENGINES 



417 



Fig. 281 {a), where it is compressed by the under side of the piston 

acting as a pump during the down stroke. The opening of 

separate inlet and exhaust valves 

is replaced by the uncovering of 

the inlet and exhaust ports by the 

piston when near the end of its 

stroke, as shown in Fig. 281 {h). 

The fresh chargeenteringthrough 

the inlet port is so baffled as to 

assist in driving the burnt gases 

toward the exhaust port. 




Fig. 281. 



204. The Diesel Engine. 

(a) Engines commercially known 
by this name operate approximately on the cycle discussed in 
Section 58, and shown in Fig. 29. The real cycle may be com- 
pleted in either two or in four strokes. 

(b) The mechanical operations within the power cylinder of 
the real engines are very similar to those of the Otto engine. 
With four-stroke operation the suction stroke charges the cylinder 
with air, which on the return stroke is compressed into a clear- 
ance volume so small that the terminal 
pressure is very high, equal to 400 to 
500, or more, pounds per square inch, 
with correspondingly high temperature. 
Just before, or when, the piston reaches 
the end of the compression stroke, a 
small quantity of finely atomized liquid 
fuel is blown into the clearance space 
by means of air at very high pressure. 
The fuel immediately ignites, due to 
the high temperature of the air that was compressed in the 
clearance space by the engine piston. The combustion which 
ensues continues a little longer than the period of injection. As 
the moving piston increases the volume a little faster than the 
gas tends to expand under the action of the heat developed, and 
as heat is lost in the cylinder walls, the upper line of the 
card slopes slightly, as in Fig. 282. In this figure the ideal and 
real diagrams are shown superimposed, with the lower loop 
exaggerated. 




Fig. 282. 



41 8 HEAT-POWER ENGINEERING 

(c) Within the past few years several designs of two-stroke- 
cycle engines operating on this cycle have been made, and some 
of these give considerable promise of success. 

205. Modifications to Suit Different Fuels. Theoretically, 
the internal combustion engines just discussed can use any fuel 
that can be introduced as gas or vapor (or even as finely divided 
solid) in a combustible mixture. In practice the fuels used are 
the combustible commercial gases, petroleum products, the by- 
product tars from gas works and such, and alcohol. It is gen- 
erally necessary to make the design of some parts of the engines 
and auxiliaries special for each different fuel, and as a result 
commercial engines are often named after the fuel used; thus 
there are " producer-gas engines," "gasoline engines," "kerosene 
engines," etc. The chief differences between types are given in 
the following sections. 

206. Compression and Maximum Pressures, (a) In prac- 
tice one of the most important considerations is the final com- 
pression pressure. In theory the thermal efficiency will increase 
with the final compression pressure, and within limits this is 
true in the real engines (see Section 219). 

It is found, however, that compression above certain limiting 
pressures causes spontaneous ignition, or preignition, which tends 
to stop the engine. 

With some fuels the spontaneous-ignition temperature and 
pressure are so high that the compression limit is not set by 
preignition, but by commercial considerations. Thus, with very 
high compression the " up-keep " may exceed the gain due to 
increased thermal efficiency. For example, engines using blast- 
furnace gas usually compress only to about 175 pounds gauge, 
or even less, although the preignition pressure is much higher, 
and the thermal efficiency of engines compressing to 200 pounds 
has been shown to be better. 

(b) The usual compression pressures (terminal) in the differ- 
ent types of engines as- now designed are given in Table XI. 
This shows that the lowest compression pressures are used with 
the fuels high in hydrocarbons, while high pressures are used 
with fuels low in these constituents. 

High compression increases the thermal efficiency, not only 



INTERNAL-COMBUSTION ENGINES 



419 



because it improves the theoretical cycle, but also because it aids 
ignition and makes combustion more rapid. This is particularly 
true with the weaker fuels, like blast-furnace gas. 

TABLE XL — COMMON COMPRESSION PRESSURES. 



Fuel. 


Comp. Press. 

Lbs. above 

Atmos. 


Fuel. 


Comp. Press. 

Lbs. above 

Atmos. 


Kerosene 

Gasoline 

Illuminating gas 

Natural gas 


5° to 75 
60 to 75 
70 to 90 
100 to 125 


Producer gas 

Blast-furnace gas 

Alcohol 


120 to 150 
140 to 175 
140 to 180 



(c) In theory, with other things equal, the greater the calorific 
value of a charge and the higher the temperature before igni- 
tion, the higher will be the maximum temperature and pressure 
attained by the combustion. In practice this is modified by 
the considerations brought out in preceding sections of this 
chapter. 

In general, engines in which the maximum pressure is high 
because of rich mixtures and high compression must be stronger 
and heavier than those using "weak" mixtures and low com- 
pressions. 



CHAPTER XXV. 

INTERNAL-COMBUSTION ENGINES (cow/.)- 
Mechanical Features. 

207. Cylinder Arrangement, (a) In the theoretical discus- 
■sion of preceding chapters, only single-cylinder, single-acting 
<engines were considered. In practice there are three principal 
reasons for making " multi-cylinder units " and for making 
" double-acting engines." These are: 

(i) The turning effort at the shaft of an internal-combustion 
-engine with one single-acting cylinder is very uneven. This 
can be partly counteracted by the use of a very heavy flywheel, 
but this is objectionable for several reasons. As a result, both 
multi-cylinder and double-acting constructions are used to give 
overlapping cycles and therefore more even turning efforts. 

(2) The power which can be obtained from a given cylinder 
depends upon the quantity of heat which can be liberated in 
that cylinder by combustion. This, in turn, depends upon the 
volume of mixture which can be contained in the cylinder, and 
hence upon the cylinder dimensions. Experience has shown 
that a cylinder diameter of from 42 to 45 inches is about as large 
as is commercially advisable with present methods of construc- 
tion and with the materials now in use. As the length of the 
cylinder cannot be increased without limit, it results that the 
maximum power that can be obtained per cylinder is limited. 

A single-acting cylinder can be constructed to develop from 
500 to 700 horse power, and when larger powers are required per 
unit, double-acting or multi-cylinder constructions must be used. 

(3) Because of the high pressure generated in gas-engine 
cylinders, the forces transmitted by the moving parts of the 
engine are very large, and these parts must be made correspond- 
ingly large. With the single-cylinder construction, the unbal- 
anced forces are of great magnitude. These can be decreased 
by a proper arrangement of several cylinders. 

420 



INTERNAL-COMBUSTION ENGINES 421 

(b) The attainment of a more even turning effort than is 
possible with a single cylinder is of such great importance that 
very few single-cylinder engines are now built in sizes above 
50 horse power, and they are seldom used in sizes above about 
25 to 30 horse power excepting for work where close regulation 
is not very important. 

An idea of the handicap under which internal combustion 
labors in this respect can best be obtained by a comparison with 
a single-cylinder double-acting steam engine. To produce as 
many impulses in a given time as an engine of this type, a single- 
acting four-stroke-cycle engine, running at the same speed, would 
require four cylinders; if double-acting, two cylinders would be 
needed. The two-stroke cycle construction gives the same num- 
ber of impulses as does a steam engine of the same type, i.e., 
single- or double-acting. 

The double-acting, internal-combustion engine, however, offers 
more difhculties in construction and operation than does a 
similar steam engine. The piston and piston rod must be water- 
cooled in order to prevent overheating, and the maintenance 
of a tight piston-rod packing is more difficult with hot gases than, 
with steam. 

208. Classification, (a) Like steam engines, the internal- 
combustion engines are classified in a number of ways. The 
principal designations, and a brief discussion of each, are given 
in the following paragraphs. Such things as center-crank and 
side-crank construction, and right- and left-hand arrangement are 
common to all kinds of engines and need not be further considered. 

(b) Internal-combustion engines are made both vertical and 
horizontal. For sizes up to about 500 to 700 horse power either 
construction is used, each having certain advantages and certain 
disadvantages. Above 700 horse-power commercial economy 
generally dictates double-acting cylinders. Very few vertical 
engines have been built double-acting, as there is considerable 
difficulty in accommodating the valves for the lower cylinder end 
in this construction, hence the larger powers are nearly always 
supplied by horizontal engines. The vertical engine has the 
advantage of occupying much less floor space than the hori- 
zontal and can be mounted on a less massive foundation. It 
is generally operated at a higher speed, particularly in the larger 



422 



HEAT-POWER ENGINEERING 




Fig. 283. 



sizes, and is usually built with an inclosed crank case so that 
lubrication can be somewhat simplified. 

(c) The cylinders of multi-cylin- 
der vertical engines are practically 
always arranged side by side and 
as close to one another as possible. 
These engines are designated as 
two-cylinder vertical, three-cylinder 
vertical, etc. A three-cylinder 
vertical engine is shown in Figs, 
283 and 284. With horizontal 
engines, however, the cylinders 
are often widely separated, giving 
what is called a twin engine. 

It is also very common practice to place two horizontal cylin- 
ders with their axes coinciding. 
When so arranged, the engine 
is called a tandem. A com- 
bination known as a twin- 
tandem double-acting is shown 
in Fig. 285. 

(d) Internal-combustion en- 
gines are sometimes classified 
according to the use to which 
they are put. Thus there are 
stationary engines, stationary 
electric lighting engines, marine 
engines, automobile engines, 
etc. From this classification 
has sprung another, an engine 
of one type being designated 
by its type name, even when 
used for a diflterent purpose. 
There are thus " auto-type 
marine engines " and " marine- 
type stationary engines." 

(e) Since certain modifica- 
tions, or different fittings, are 
necessary with different fuels, internal-combustion engines are 
sometimes classified according to the fuel which they are intended 




Fig. 284. 



INTERNAL-COMBUSTION ENGINES 423 

to use. Thus there are kerosene engines, gasoHne engines, illumi- 
nating-gas engines, producer-gas engines, etc. 

(f) These engines are also occasionally classified on the basis 
of the type of governing used (see sec. 212). Thus there are hit- 
and-miss engines, throttling engines, etc. 




Fig. 285. 

209. Methods of Producing Combustible Mixtures, (a) With 
fuels initially gaseous, a " mixing valve " is generally used to 
control the proportions of fuel and air, the two gases being made 
to mix intimately either before or during entrance to the cylinder. 
This mixing valve may be incorporated with the inlet valve or 
it may be separate and at some distance from it. Examples of 
both types are given later. 

(b) Fuels initially liquid must either be atomized or vaporized 
and mixed with air to support combustion. With the more 
volatile liquid fuels, such as gasoline and alcohol, the process 
generally takes place outside of the engine cylinder in a " carbu- 
retor"; the mixture then passes to the cylinder as in the case of 
fuel initially gaseous. With the less volatile liquid fuels, like 
kerosene or crude oil, vaporization and mixing are more difficult, 
and generally take place within the engine cylinder, the fuel 
being sprayed in either by pump or air pressure and being 
vaporized by heat from hot walls or gas. Examples of such 
devices are given later. 

210. Carburetors, (a) When an engine uses a volatile liquid 
fuel, like gasoline or alcohol, it is customary to mix the fuel vapor 
and air outside of the cylinder in a carburetor, in which air, 
which may or may not be previously heated, is brought into 



424 



HEAT-POWER ENGINEERING 



intimate contact with the Hquid and becomes charged with the 
vapor. 

(b) A great variety of types of carburetors has been per- 
fected and used. Thus there are bubbling carburetors, in which 
some or all of the air is made to pass or bubble through the 
volatile liquid, on its way to the engine. There are surface 
carburetors, in which the volatile liquid is spread over screens, 
marbles, or anything else which will give a large wetted surface 
over which the air may be drawn. Wick carburetors have also 
been used. In these the liquid is drawn up into wicks by capil- 
lary action, and the air passing over the surface of the wicks 
vaporizes part of the exposed liquid. 

(c) Practically the only type now used in this country is the 
jet carburetor. This apparatus is made in many forms, but the 
fundamental principle of all is the same. A fine jet of gasoline 
is injected into the air pipe and generally only during the suction 
stroke. The impelling force is usually either the pressure due to 
a slight head of gasoline or the difference between suction pres- 
sure and atmospheric pressure, or this difference augmented by 
the suction effect of rapidly moving air upon a nozzle immersed 
in it. 

(d) One of the most common types of jet carburetor, known as 
a carbureting valve, is shown in Fig. 286. The valve is some- 
times the inlet valve of the 
cylinder, but more often it is a 
separate valve through which 
air is admitted to the mixture 
pipe leading to the main inlet 
valve. A small hole is drilled 
in the seat of the carbureting 
valve in such a position that it 
is closed when the latter is 
seated. When the valve rises 

(automatically) to admit air to the engine, the liquid under slight 
pressure issues from the hole in a very small stream, which mixes 
with the air and is partly or wholly vaporized before the mixture 
enters the cylinder. 

(e) Another form of jet carburetor is shown in Fig. 287. The 
liquid is maintained at such a height that its surface almost 
reaches the tip of the spray or injection nozzle when quiescent. 




Fig. 286. 



INTERNA L-COMB USTION ENGINES 



425 



The air passing around this nozzle on its way to the engine creates 
a partial vacuum at the nozzle, which vacuum augments the 
lowering of the pressure caused by suction in the engine. The 
air pressure on the surface of the liquid in the small tank then 
forces a fine jet out of the nozzle, and this is picked up by the 
surrounding air. The throat, or Venturi tube, increases the 
velocity of the air flowing through it, which materially assists in 
picking up and carrying the liquid during vaporization. This 
type is commonly used on stationary engines, the liquid level 
being maintained by a direct-connected pump and overflow as 
shown. 





Fig. 287. 



Fig. 288. 



(f) In Fig. 288 is shown a type of float-feed carburetor. This 
is similar in action to that last described, the principal difference 
being the float for maintaining the proper liquid level. This 
operates by opening and closing the small valve shown as the 
liquid level sinks and rises, the liquid being supplied to this 
valve under pressure. 

This type of carburetor is most common on automobile and 
marine engines, the central float, which maintains approximately 
the correct level despite tipping of the carburetor, and the 
compact structure both recommending it for such purposes. 

(g) When an engine is run at widely varying speeds, it is a very 
difficult matter to adjust a carburetor of the type last shown to 
give a suitable mixture under all conditions. If the mixture is 
correct at low speeds, it is apt to be too rich at high speeds. 
This is overcome by introducing an auxiliary air valve between 
the spray nozzle and the engine This valve, operating auto- 
matically or under hand control, admits air, which, combining 
with the over-rich mixture, forms one of correct proportions. 



426 



HEAT-POWER ENGINEERING 



Similar devices are sometimes necessary with the carburetor 
used on engines which run at a constant speed, being used to 
make the adjustment of the carburetor easier or more certain, 

211. Treatment of Heavy Oils, (a) The use of fuels Hke 
kerosene, distillate, crude oil, and such, presents greater difficulty 
than the utiUzation of gasoline or alcohol. Kerosene can be 
handled more or less satisfactorily with carburetors similar to 
those described, but, being less volatile than gasoline, the action 




is not so perfect. It is generally necessary to preheat the air 
and to jacket the mixture pipe with hot jacket water, or with 
exhaust gases. Even with these additions, it is often found 
difficult to operate satisfactorily, and most carbureting kerosene 
engines are arranged to spray water into the cylinder or to satu- 
rate the mixture with water vapor on its way to the cylinder, 
particularly when running under heavy loads. Just what the 
action of the water vapor may be is still undetermined, but it 
seems to give more certain, quieter, and cleaner combustion. 

(b) Many kerosene and other oil engines operate on what 
is known as the hot-bulb or hot-head principle. An engine of this 
type Is shown in Fig. 289. 

The oil Is Injected into the hot bulb during the suction or com- 
pression strokes and is there vaporized by the hot walls. Air 



INTERNAL-COMBUSTION ENGINES 427 

Is compressed into the bulb during the compression stroke of the 
engine, and, when the mixture acquires the proper proportions, 
spontaneous ignition takes place. The bulb is heated to redness 
by a blow-torch before starting the engine, and thereafter is main- 
tained at the proper temperature by the heat generated during 
combustion. 

There is always a certain amount of carbon or lampblack 
deposited within the hot bulb by the " cracking " of the oil 
molecules during vaporization, and it is therefore necessary to^ 
clean the bulb periodically. 

(c) Practically the only other distinct method of using the 
heavier oil fuels in internal-combustion engines is that exemplified 
in the Diesel oil engine described in Section 204. This gives by 
far the most perfect combustion with the heavier fuels, but is open 
to criticism because of the high pressures involved. 

(d) To overcome this difificulty, engines are now being built 
which may be considered a compromise between the hot-bulb 
and the Diesel types. The pressures are lower, but the hot bulb 
insures successful ignition and combustion. These engines are 
proving highly economical in the use of fuel, and can be kept in 
good mechanical condition with greater ease than can the high- 
pressure Diesel engine. 

212. Methods of Governing Internal-Combustion Engines. 

(a) Stationary engines are generally mechanically regulated to 
maintain approximately constant speed of rotation. Automobile 
and marine engines are commonly hand-governed, although they 
are sometimes fitted with a limit governor to prevent over- 
speeding, or ''racing.'' 

(b) In order to govern or regulate an engine, the i.h.p. must 
be varied to suit the demand, as shown in Section 134. There 
are three available methods of doing this: (i) The amount of 
energy made available per cycle may remain constant, but the 
number of cycles per unit of time may be changed; (2) the num- 
ber of cycles may remain constant and the amount of energy 
made available per cycle may be varied; and (3) a combination, 
of the two preceding may be used. 

(c) In general, there are four different ways of applying these 
methods. They are called : (1) hit-and-miss governing, (2) quan- 
tity governing, (3) quality governing, and (4) combination sys- 



428 HEAT-POWER ENGINEERING 

terns. These are each considered in detail in the following 
paragraphs. 

(d) In hit-and-miss governing, the number of working cycles 
per unit of time is varied so as to adjust the average i.h.p. to 
the demand for power. With this system, some part of the 
mechanism for opening the inlet valve is under the control of 
the governor, so that when a " working cycle " is to occur it hits 
another part and opens the valve, but when the cycle is to be 
omitted it misses engagement and the valve remains closed. 
When a miss occurs, not only does the inlet valve remain closed, 
but the exhaust valve is usually held open, so that, during the 
strokes corresponding to the ordinary cycle, the piston pumps 
exhaust gas into and out of the exhaust pipe without waste of 
energy, except for the slight friction and heat loss. 

In some engines, when the working cycle is to be omitted, a 
fuel valve, which is separate, is held closed while the inlet and 
exhaust valves act as usual; thus the piston draws in a charge 
of pure air, which it compresses, expands, and exhausts. This 
method is generally considered less satisfactory than the former, 
because of the cooling effect oh the cylinder walls. 

With hit-and-miss governing all working cycles are theoreti- 
cally exactly alike, and are equal to the maximum for the 
particular engine. As all types of internal-combustion engines 
show greatest thermal efficiency when developing normal cycles 
of about maximum power, this method of governing has the theo- 
retical advantage of giving high thermal efficiencies at all loads. 
The cycles actually produced, however, are not all alike, because 
of irregular cooling and heating effects, the varying mixtures 
resulting from intermittent operation, etc. The variations 
become more marked with increase of the number of misses, and 
the method therefore gives lower efficiencies at light loads than 
would be expected. In general, however, it is the most economi- 
cal method of governing yet devised. As considerable intervals 
of time may intervene between "working" cycles, a very heavy 
flywheel is needed on engines governed by this method. 

Hit-and-miss governing is very satisfactory for engines where 
■close speed regulation is not necessary, and is commonly used 
on the smaller sizes, say up to 25 or 50 horse power. Where 
close regulation is required, as for the operation of alternators 
in parallel, it is practically never used. 



INTERNAL-COMBUSTION ENGINES 



429 



(e) In quantity governing, the number of cycles and the pro- 
portions of the mixture are maintained constant, but the amount 
of mixture admitted per cycle is varied to suit the power demand. 
This is generally done in one of two ways, — by "cut-off gov- 
erning," or by " throttling governing." 

In cut-off governing, after the amount of mixture necessary to 
produce the required power has been taken in, the inlet valve 
is closed, and the charge expanded as the out stroke, or suction- 
stroke, continues. The cycle is then completed as usual, produc- 
ing under low load a diagram like that of Fig. 290, in which the. 
lower loop is exaggerated for clearness. 




Fig. 290. 




Fig. 291. 



In throttling governing, except at the maximum load, the 
charge is throttled during the entire suction stroke to reduce 
the amount of mixture entering the cylinder. This gives a dia- 
gram like Fig. 291, in which the lower loop is again exaggerated. 

In both of these methods of governing, the reduction in quan- 
tity of mixture with decrease in load is accompanied by a lower- 
ing of the compression curve. If not carried too far, this is 
desirable from a mechanical standpoint, as it tends to produce 
more uniform turning effort, and reduces the necessary weight 
of flywheel. 

Of the two methods the cut-off is the better because it gives 
a smaller lower loop and less lost work. It also has the advan- 
tage that the governor action is delayed to the latest possible 
instant in the cycle, and hence each working cycle more nearly 
meets the power demand. 

(f) In quality governing the number of cycles and quantity of 
material per cycle are maintained constant, but the proportion 
of gas to air, or quality of the mixture, is varied, so that the 
power developed in the cylinder just meets the power demand. 

Since the same volume of mixture is drawn in each cycle and 
is compressed to the same pressure, the efiticiency is theoretically 




430 HEAT-POWER ENGINEERING 

constant at all loads. In practice, however, each fuel has an 
air-to-gas ratio that gives best results; thus it follows that this 
method of regulation gives maximum efhciency only at one 
particular load. With some fuels it is exceedingly difficult to 
obtain satisfactory ignition of the very " weak " mixtures intro- 
duced at low loads, and such 
mixtures also burn very slowly, 
the combustion continuing in 
extreme cases throughout the 
entire expansion stroke. 

A group of indicator diagrams 

Fig. 292. from a quality-governed engine 

is given in Fig. 292. The slow 

turning of the weak charges is shown by the gradual tilting of 

the combustion line as the load decreases. 

The constant compression pressure has an undesirable effect 
on the crank effort (see (e) of this section), as the m.e.p. of the 
compression line does not change with the m.e.p. of the expansion 
line. 

(g) Combined systems are sometimes used in an effort to 
obtain the advantages of the different methods previously 
described with as few as possible of their disadvantages. Thus 
hit-and-miss governing may be used at low loads and quality 
governing at the higher loads which call for sufficient gas to 
make a readily ignitable mixture. Or quality governing may be 
used at the higher loads, gradually merging into quantity govern- 
ing as the load decreases. 

All these combinations tend to complicate the valve gear and 
call for more or less sensitive and intricate adjustments. They 
are, therefore, commercially handicapped, though theoretically 
desirable. 

(h) As the form and area of the card may be changed by 
altering the time of ignition, this might be used for governing. 
It is actually used for that purpose to a certain extent in marine 
and auto engines. Since there is some best time of ignition for 
each mixture in each engine running at each speed, it is generally 
better to change the time of ignition to suit the conditions 
brought about by governing rather than govern by changing the 
time of ignition. 

In some combination systems an ignition timing device under 



INTERNAL-COMBUSTION ENGINES 



431 



control of the governor has been incorporated, but it has gener- 
ally been found more satisfactory to trust to hand timing. 



213. Gas Valves, Mixing Valves, etc. (a) When gas is sup- 
plied an engine under pressure, as is generally the case in all 
except "suction gas-producer" plants (see Fig. 5), a gas valve of 
some sort is necessary to shut off the gas supply during all but 
the suction stroke of the engine. 

(b) This valve may be combined with the inlet valve of the 
engine, giving the arrangement shown diagrammatically in 
Fig. 293. The air and gas cocks shown are used for proportion- 
ing the mixture by hand, and the gas cock is also used as a 
permanent shut-off valve. Such an arrangement can be used 
with hit-and-miss or with quantity governing, but is obviously 
unsuited for quality governing because of the hand regulation 
of the proportions. 



Inlet 
Valve 





(c) The gas valve is more commonly a separate valve, although 
it may be carried loosely on the same stem as the inlet valve, 
as a in Fig. 294. When thus made separate from the inlet valve, 
it can be put under governor control, so that any kind of govern- 
ing can be adopted, at the option of the designer. In all cases 
it is common practice to supply gas and air cocks or their equiva- 
lent so that the proportions of the mixture can be roughly regu- 
lated by hand and so that the gas can be permanently shut off 
from the engine. 

(d) The terms mixing valve and proportioning valve are used 
rather loosely to designate anything which has to do with the 
mixing of air with gas already measured out, or with the measur- 
ing and mixing of the constituents of the charge. In the strictest 



432 HEAT-POWER ENGINEERING 

sense a proportioning valve, and to a certain extent a mixing 
valve, precedes the inlet valve, measures the combustible part 
of the charge, and mixes it with the air. A gas valve under 
governor control, combined with surfaces, or passages, which will 
mix the gas with the air before or during passage through the 
inlet port, is properly a mixing or proportioning valve. One 
example of this sort of arrangement is shown in Fig. 294. 

The small gas valve a is guided by the sleeve sliding on the stem 
of the inlet valve b. It is operated by separate linkage under 
governor control, so that the time, or extent, of its opening can 
be varied to suit the load. In operation, the inlet valve opens 
first, allowing fresh air to enter the cylinder and blow away hot 
burned gases. The gas valve a then opens, admitting gas, 
which, traveling downward, is thoroughly mixed with the air 
as it issues from the small holes shown. The vaive a closes 
before the inlet valve b, so that the mixing chamber becomes 
filled with pure air before being shut off from the cylinder. 

Such a device is commonly known as a combined mixing and 
inlet valve, although the gas valve is occasionally designated as a 
mixing valve or a proportioning 
valve. 

(e) The elements of another type 
of mixing valve are shown in Fig. 
295. The inner cylinder is supposed 
to be under governor control, so that 
it can be rotated more or less as the 
load varies, thus changing the effect- 
ive openings of the gas and air ports 
to suit the demand for power. By 
properly proportioning the gas and air ports, their areas may be 
made to change at the same rate under the action of the governor, 
thus giving throttling regulation; or the areas may be made to 
change differentially, giving quality governing or mixed quality 
and quantity regulation. 

(f) Experience has shown that proportioning valves of the type 
shown in Fig. 295, and others using sliding surfaces, are per- 
fectly satisfactory when used with such fuels as natural gas and 
illuminating gas. Producer gas and blast-furnace gases, how- 
ever, carry impurities which quickly foul such sliding surfaces 
and impair the action of the valve. For such gases, mixing and 




INTERNAL-COMBUSTION ENGINES 



433 



proportioning valves made without sliding surfaces, such as that 
shown in Fig. 294, must be used. Even the valve shown in this 
figure might give trouble because of deposits on the stem of the 
main valve, and a design eliminating this possibility would prob- 
ably give better results. 

214. Methods of Ignition, (a) In the early development of 
gas engines the charge was ignited by opening communication 
at the proper time between the compression space of the engine 
and a small chamber containing an open flame. This method 
was complicated mechanically, and had so many objectionable 
features that it did not survive. 

(b) The methods at present used are: 
(a) Hot- tube ignition ; 

{h) Spontaneous ignition by heat of compression (as- 
sisted, or not assisted, by the action of a hot cham- 
ber, such as a vaporizer or hot bulb) ; 
(c) Electric ignition. 



215. Hot- Tube Ignition, (a) A simple type of hot- tube igni- 
tion is shown schematically in Fig. 296. The tube a, generally 
made of metal, is closed at one end, while 
the other end opens into the cylinder. 
By moving the burner and chimney h, 
the hot zone, which is at about red heat, 
can be located anywhere along the tube. 

At the end of the exhaust stroke the hot 
tube, like the rest of the clearance space, 
is filled with burned gases at a pressure 
slightly above atmospheric. During the 
suction stroke these gases are partly ex- 
panded, and during the compression 
stroke they are compressed into the tube 
by the combustible mixture until the lat- 
ter finally reaches the hot zone, where it 
is ignited. By moving the hot zone along the tube, the time in 
the compression stroke at which the mixture is ignited can be 
varied. 

(b) By this method ignition is generally certain, but the timing 
is untrustworthy because of variations in the condition of the 




Fig. 296. 



434 HEAT-POWER ENGINEERING 

tube or of the mixture. Hence, despite its simplicity and lack 
of moving parts, hot- tube ignition is not now very widely used. 
" Timing valves " have been used to close the cylinder end of 
the tube and to thus control ignition, but few have survived. 

Hot-tube ignition involves a constant supply of gas to the 
burner, and this of course adds to the fuel consumption of the 
engine. 

216. Spontaneous Ignition. In many engines using liquid 
fuels heavier than gasoline, ignition is produced by the tem- 
perature attained during compression. In the Diesel engine 
the compression pressure is so high that the resulting temperature 
alone causes ignition. In other engines, like the hot-bulb type 
(Fig. 289), ignition results from the combined action of compres- 
sion and a hot vaporizing chamber. 

This method of igniting has not proved applicable to the more 
volatile liquid fuels and to the gaseous fuels because of the diffi- 
culty of timing. 

217. Electric Ignition, (a) The most satisfactory method of 
igniting is by an electric spark. 

All electrical ignition systems in use, with few exceptions, 
fall under either " make-and-break " or "jump-spark " ignition. 
The less descriptive terms, " low- tension " ignition and " high- 
tension " ignition, are often used in place of these. 

(b) In the make-and-break ignition system, two " electrodes " 
are brought together within the combustion space to " make," or 
close, the circuit, and are separated suddenly to "break" the 
circuit and produce a spark. 

One arrangement of such a system is shown in Fig. 297, the 
". igniter block" or "plug," entering the combustion space through 
the center of the cylinder head. The " stationary electrode " 
is designated by i and the "movable electrode" by j. The wir- 
ing diagram is shown in Fig. 298. In this figure, B represents 
a battery or other low- voltage generator, C an "induction " or 
" intensifier coil," E the stationary electrode, which is insulated 
from the igniter block and engine frame, and 6" a stud or other 
convenient screw fastening on the engine. The movable elec- 
trode is in electrical contact with the igniter block and engine 
frame, as shown in Fig. 297. 

(c) The operation is as follows: The cam a, Fig. 297, pushes 



INTERNA L-COMB U ST ION ENGINES 



435 



the rod h toward the igniter and the strike block d, engaging the 
flipper e on lever /, moves the latter toward the left. As / 
moves, it draws g after it by means of the one-turn spring shown. 
As g moves it rotates the movable electrode until the arm j 
inside of the cylinder is brought into contact with the stationary 




Fig. 297. 

electrode i. The circuit is then made and current flows until 
the circuit is broken by the block d traveling past the edge of the 
flipper e. When this occurs, the spring h pulls the arm j out of 
contact with i, and the circuit is broken. The spark results 
from the action of the induction coil at the instant of breaking 
the circuit. The rapid change in the number of lines of force 




Fig. 298. 

through the core causes sufficient self-induction to generate an 
electromotive force of such intensity as to bridge the gap between 
the separating electrodes. 

(d) The timing of the spark is effected by moving guide C 
across the path of the bar h in Fig. 297, thus changing the time 
at which block d releases flipper e. 

(e) The type of igniter just described is known as a " hammer 
make-and-hr eak igniter " to distinguish it from another known 



436 



HEAT-POWER ENGINEERING 



as a " wipe-spark " or " wipe make-and-hreak igniter, ^^ in which a 
movable electrode periodically wipes or slides across a station- 
ary electrode. The wipe spark automatically cleans the contact 
surfaces within the cylinder, which is in a way advantageous, 
but it is not so extensively used as the hammer type. 

(f) The make-and-break system has the advantages of being 
electrically simple and operating with low e.m.f., so that short 
circuits are not so apt to occur as in the systems described in 
following sections. It is, however, complicated mechanically, and 
because of friction and inertia of parts is not generally used on 
engines operating at speeds above 500 to 600 r.p.m. The 
movable electrode is very apt to stick or to work loose, causing 
trouble because of no spark or because 
of loss of compression by leakage. 

(g) In the jump-spark system there 
are within the cylinder two fixed termi- 
nals, with short intervening gap, across 
which a spark jumps when sufficient 
difference of potential has been devel- 
oped. In its simplest form the apparatus 
has two circuits, as shown in Fig. 299, 
with heavy lines representing the "low-tension circuit " and the 
light lines the "high-tension circuit.'^ 




Fig. 299. 




Fig. 300. 



In the figure, B is the source of electromotive force, 7" is a 
rotating "timer," C a "condenser," K a "coil," and S a 
" spark plug," several examples of which are shown in Fig. 300. 



INTERNAL-COMBUSTION ENGINES 437 

(h) In operation the primary circuit is closed by the timer T 
and then suddenly opened, with the result that a spark jumps 
between the terminals of the plug. The action of the coil is 
as follows: When the primary circuit is closed by rotation of 
the timer, the magnetic field induces an electromotive force in 
the secondary circuit. This is not great enough, however, to 
cause a spark to pass between the plug terminals. But when 
the primary circuit is quickly broken, the sudden collapse of the 
magnetic field about the core of the coil induces for the instant 
in the secondary circuit a very high potential difference, which 
may be made sufficient to cause the passage of a spark, with 
resultant ignition. 

The function of the condenser, which bridges the timer in the 
primary circuit, is to prevent sparking at the contact points of 
that apparatus. Such sparking would cause rapid deterioration 
of the contact surfaces and is therefore undesirable. 

(i) A more common type of jump-spark apparatus uses a 
" trembler coil " instead of the plain induction coil shown in 
Fig. 299. This apparatus is so arranged that the trembler forms 
part of the primary circuit, and is in such position that it is at- 
tracted to the core of the coil when this is magnetized, and thus 
breaks the primary circuit. This in turn demagnetizes the core, 
hence the trembler flies back and makes the circuit once more; 
thus the core is again magnetized and attracts the trembler, 
breaks the circuit, and so on, as long as the timer is in position 
to close the primary circuit. This intermittent making and 
breaking of the primary circuit causes a succession of sparks 
at the spark plug in the secondary circuit, which action is generally 
supposed to insure more certain ignition. The great advantage 
achieved is really quick action and accurate timing, though 
these are often counterbalanced by considerable trouble with the 
trembler which may call for almost constant adjustment. 

(j) Both of these high-tension or jump-spark systems are 
easily timed by shifting the phase relation of timer, or commuta- 
tor, and engine crank, and they are particularly satisfactory for 
high speed. Recently there has been a tendency to adopt these 
systems for ordinary slow-speed stationary work; but as the 
spark does not seem to have the same igniting power as that of 
the make-and-break system, most applications have been limited 
to the more easily ignitable fuels like natural and illuminating 



438 



HEAT-POWER ENGINEERING 



gas and gasoline. Few simple high-tension systems have yet 
been used with producer gas and " blast-furnace gas." 



218. Internal-Combustion Engine Valve Gear, (a) The slide 
valve, so common in steam-engine practice, is never used in its 
simple form on internal-combustion engines for admission or 
exhaust. It is sometimes used for mixing purposes, as was 
indicated in Sect. 213. The high temperatures to which inlet 
and exhaust valves are subjected make lubrication difficult and 
cause warping of the valve and seat, and the high pressures make 
it difficult to keep the valve on its seat to prevent leakage. When 
the fuel used contains sulphur, which is not an uncommon 
occurrence, the valve and seat are often 
quickly pitted and corroded. 

(b) Some highly specialized slide valves 
are, however, in use and give good satis- 
faction. The control of ports by the 
piston of the two-stroke-cycle engine is 
the most common example. Recently a 
number of " sleeve motors " have been 
designed for use on automobiles and seem 
to promise very satisfactory operation. 

One example of this type is shown 
semi-diagrammatically in Fig. 301. The 
two sleeves, reciprocating vertically un- 
der the action of eccentrics or cranks on 
a side shaft, act in conjunction with the 
cylinder head and external cylinder to 
control admission and exhaust by means 
of the ports shown. The advantages of 
this type are rapid opening and closing of valves, long period of 
approximately maximum opening, and silent operation. 

(c) The success of this type of valve has caused the appear- 
ance of a number of different varieties of slide-valve and piston- 
valve auto-engine designs. Few of these have been tested to 
any extent, and it is therefore too early to draw conclusions as 
to their ultimate success. 

(d) With the exception of the cases cited above, the poppet 
or mushroom valve is in practically universal use for internal- 
combustion engines. It maintains its correct shape under 




Fig. 301. 



INTERNAL-COMBUSTION ENGINES 439 

changing temperatures more perfectly than other types; it re- 
quires a minimum of contact surface between valve and seat; 
it opens inward and is therefore forced to its seat by the high 
pressures in such engines; it requires no lubrication; and it and 
its seat are easily kept comparatively true by grinding. 

(e) In modern designs, inlet valves are practically never 
water-cooled, as the ingoing charge cools them sufficiently during 
each suction stroke. Exhaust valves, on the other hand, are 
practically always water-cooled when larger than five inches 
in diameter, and often in smaller sizes. This is deemed necessary 
because of the high temperature of the exhaust gases in which 
the valve is immersed during the entire exhaust period, but it 
should be noted in this connection that one European builder 
is obtaining satisfactory operation with simple uncooled cast iron 
exhaust valves in the largest sizes of horizontal engines. 

(f) In some four-stroke-cycle engines the operating condi- 
tions of the exhaust valve have been improved by the use of 
" auxiliary exhaust ports.'' These are ports in the cylinder wall 
which are uncovered by the piston when near the end of its 
stroke. The first discharge of exhaust gases takes place through 
these ports, so that a smaller quantity of cooler gases is handled 
by the exhaust valve. 

This construction necessitates the use of a larger cylinder for 
a given power than is required without the use of auxiliary 
ports, and it complicates the cylinder casting. It is practically 
never used on double-acting engines because of these reasons, and 
because of the additional fact that it would necessitate the use 
of an enormously long piston, similar to that shown in Fig. 280, 
thus materially increasing the weight of the reciprocating parts. 

(g) Two types of inlet valve are in use, — the automatic valve 
and the positively actuated valve. The automatic valve is held to 
its seat by a weak spring, and is raised by the difference between 
atmospheric and suction pressures during the suction stroke. 
The positively actuated valve is opened mechanically and gen- 
erally closed by spring pressure. 

Automatic valves are uncertain in their action, opening only 
after a considerable pressure difference has been created, and 
then more or less slowly. After opening they do not remain 
wide open during the remainder of the suction stroke, but 
" chatter " more or less, thus materially decreasing the volu- 



440 



HEAT-POWER ENGINEERING 



metric efficiency of the engine. For these reasons they are 
seldom used on the better types or on the larger engines. 

Positively actuated valves, on the other hand, can be made 
to open at the time desired, can be given an amount of opening 
approximately equal to that theoretically required at each piston 
position, and can be made to close very nearly at the right time. 

(h) The valves of internal-combustion engines are generally 
operated by means of cams, or eccentrics, on a side shaft, or 
auxiliary shaft, driven by gearing from the crank shaft. On 
the smaller engines cams are most often used, but on the larger 
engines the eccentrics seem to be preferred, particularly in this 
country. Closure practically always occurs by spring pressure, 
the valve being released by the opening mechanism. 

The cam can be manufactured more cheaply than the eccentric, 
and when properly designed it is not very noisy in operation and 
wears slowly. In general, however, it is rather difficult to 
obtain as perfect valve operation with cams as it is with eccentrics 
unless" linkage is introduced, which complicates the mechanism 
and increases the cost. 






Fig- 303- 



Fig. 304. 



Cams may be used to operate the valves by direct contact 
with the valve stem (Fig. 302) ; or by contact with one end of a 
pivoted lever, the other end of which contacts with the valve 
stem (Fig. 303) ; or through rolling, rocking, or floating levers, one 
arrangement of which is shown in Fig. 304. 

The eccentric always operates in conjunction with such levers 
as are shown in Fig. 304. 



INTERNAL-COMBUSTION ENGINES 441 

(i) The time (with reference to crank and piston positions) 
at which valves open and close varies widely with the location 
of the valve and with the type of engine. The exhaust valve 
universally opens early, generally when the piston is at about 
0.9 stroke. It may close before the end of the return stroke, or 
on dead center, or it may remain open until after the suction 
stroke has started. The object of leaving it open after dead 
center has been passed is to take advantage of the inertia of the 
moving exhaust gases and thus get more perfect discharge. 
Where the valves, manifolds, and cylinders are so arranged that 
this can be done, it represents good practice. The inlet valve 
very commonly opens after the beginning of the suction stroke, 
though it is sometimes opened just before, or on dead center, in 
order to obtain a wider opening by the time suction actually 
starts. It is very generally closed after the end of the suction 
stroke in order to take advantage of the inertia of the moving 
column of gas, thus increasing the volumetric efhciency. 

In general, the higher the speed of an engine the later may the 
valves close, and the greater may be the overlap of exhaust 
closure and inlet opening if the valves are widely sepa- 
rated. 

(j) Because of the heavy springs necessary to close the valves 
of internal-combustion engines in the short time available, and 
because of the relatively great weight of the valves, the parts 
actuating the latter are generally very strong and heavy. This 
is particularly true of exhaust- valve gear. This valve must be 
opened against the combined action of high-pressure gas and a 
very powerful spring. 

Many designers have attempted to reduce the size and wear 
of the actuating parts by building balanced exhaust valves. As 
a general rule these have not survived, probably because they 
simplify the external gear by complication of the inclosed part 
of the valve system. 

Because of the great weight of the valves and actuating 
mechanisms in large engines and because of the great magnitude 
of the forces transmitted by these mechanisms, it is generally 
undesirable or even impossible to construct governors which 
can operate in any such direct manner as is common in the 
average steam engine. Governors could not be constructed 
powerful enough to operate directly unless made with such 



442 HEAT-POWER ENGINEERING 

heavy parts, and to transmit such great forces, that their sensi- 
tiveness would be considerably impaired. 

In very large engines a differential governing device is now 
commonly used. In such cases the governor operates upon the 
equivalent of a small engine of some kind, which engine, in turn, 
supplies such power as is necessary for moving the valve gear. 
As an example, the governor might actuate a small pilot valve 
which by its motion admitted oil under pressure to one, or the 
other, end of a cylinder fitted with a piston suitably linked to 
the inlet- or mixing- valve gear. The motion of the piston in the 
proper direction and to the right extent, as controlled by the 
governor through the pilot valve, would then serve to give the re- 
quired adjustment of the main valves. 

In smaller engines it is customary to connect the governor 
to some light form of mixing valve, to a balanced or floating 
valve of some kind, or to a light link or equivalent which is 
easily moved and causes the necessary adjustment by the shifting 
of a fulcrum or the like in the main gear. 



CHAPTER XXVI. 

INTERNAL-COMBUSTION ENGINES (cont.). 

Efficiency, Performance, and Power. 

219. Efficiencies of Otto Four-Stroke Cycle Engines, (a) Not 
only does the thermal efificiency of the Otto cycle engine theo- 
retically vary with the ratio of compression, increasing as the 
final volume is decreased with respect to the initial volume, 
but real engines also show a similar gain. The rapid improvement 
in the efficiency of this type of engine during the past twenty 
years has been largely due to this increase in compression pres- 
sure. It is well shown by the following table:* 



TABLE XII 


— EFFICIENCIES OF OTTO FOUR-STROKE 
ENGINES. 


CYCLE 


No. 


Year. 


Type of 
Engine. 


Cylinder 
Size. 


Indicated 

Thermal 

Efficiencies. 


Brake Thermal 
Efficiencies. 


Mechanical 
Efficiencies. 


I 

2 

3 
4 


1882 
1888 
1898 
1908 


Deutz 
Crossley 
National 
Crossley 


Inches. 
6.75X13.7 
9-5 X18 

ID X 18 

II. 5 X21 


Per cent. 
16 
22 

28.7 
36.8 


Per cent. 
14 

18.9 
25 
32.2 


Per cent. 
87.6 
86.1 
87.0 
87.5 



(b) It should not be assumed, however, that by an indefinite 
increase of compression pressure the thermal efficiency of the 
real engine can be raised without limit. For even if the ten- 
dency of the fuel to preignition could be overcome, calculations 
based upon actual performances show that with the Otto type 
of engine the maximum practical thermal efficiency would 
probably be attained with a compression pressure of from 250 
pounds to 300 pounds per square inch. 

Blast-furnace gas engines operating with compression pressure 
as high as 200 pounds have given thermal efficiencies on the 
brake of 32 to 34 per cent. But the tendency with this fuel is 
* The Gas, Petrol and Oil Engine, D. Clerk, page 243. 
443 



444 HEAT-POWER ENGINEERING 

now toward the use of compression pressures in the neighborhood 
of 1 60 to 180 pounds because of the mechanical difficulties 
encountered with the higher pressures; and in this case a little 
under 30 per cent is extremely good thermal efficiency on the 
brake for modern engines, while the average operating value for 
good standard American types of stationary engines is about 25, 
to 27 per cent at rated load, and of course decreases with reduc- 
tion in the load. 

(c) Besides the compression ratio, the thermal efficiency in 
general can also be increased by 

(i) Mixing the incoming charge more perfectly; 

(2) Producing fairly rapid and complete combustion at the 

compression end of the stroke (note, however, that 
too rapid combustion is not desirable) ; 

(3) Preventing loss of heat from the charge to surrounding 

metal during combustion and expansion. 

Many modern engines have elaborate mixing valves which 
cause thorough intermixing of gas and air before, or just at the 
time of, entering the cylinder. 

In high-efhciency engines the combustion space is made as 
nearly as possible spherical, hemispherical, or in the form of a 
short cylinder; and all pockets leading out of this space are 
avoided as far as possible. This results in less surface for the vol- 
ume inclosed, and thus reduces heat loss to the metal and makes 
the combustion more rapid and complete for a similar reason. 

In pockets connecting with the combustion space the gases 
often burn long after combustion of the main part of the charge 
is complete. This can be prevented by placing the igniter in 
the pocket, and igniting the gas there first, in which case the rapid 
increase of temperature will cause a sudden pressure rise, blowing 
some of the burning gas into the main charge, thus causing very 
complete inflammation. 

Large engines generally have slightly higher thermal efficien- 
cies than small engines of the same type and proportions, because 
large cylinders have less wall surface per unit of volume inclosed 
than have small cylinders of the same proportions. This, how- 
ever, may be counteracted by difficulty of mixing the charge in 
the larger cylinder and difficulty in effecting rapid and complete 
combustion. 

When large cylinder diameters are used, two or more igniters 



INTERNAL-COMBUSTION ENGINES 



445 



at different points are often operated simultaneously in each 
combustion space in order to reduce the distance through which 
inflammation must progress from each igniter. 

Piston speeds of high-efficiency engines are carried as high as 
is mechanically feasible in order to reduce the time of contact 
between hot gases and walls. 

(d) The values of all the different efhciencies enumerated in 
Sect. 105 will vary considerably with the conditions, fuel, mix- 
ture, type of engine, etc. ; but for the purpose of giving a gen- 
eral idea of the order of these values a certain type and set of 
conditions will be assumed. 

The engine is supposed to operate with "producer gas" as 
fuel and (in the ideal case for drawing the air card) to have a 
suction pressure equal to atmospheric, a pressure of 150 pounds 
per square inch absolute at the end of compression, a temperature 
at the end of suction stroke equal to 520° F. abs., a tempera- 
ture at the end of compression of 1000° F. abs., and a tempera- 
ture at the end of combustion of about 6500° F. abs. These figures 
are obtained by neglecting all losses in the real engine and by 
considering the specific heats constant. 

(e) The thermodynamic or Carnot efficiency is then 

Ti - Ta ^ 6500 - 520 
Ti 6500 



Efc 



92 per cent. 



(f) The cycle efficiency for this Otto cycle is from Eq. (80), 
1 — - — = 48 per cent. 



CEf=l-^ 



520 
1000 



Then in Fig. 305, drawn to 
scale for the assumed engine, 
the distance AB is 48 per cent 
of^C. 

Thus the Otto cycle upon 
which this engine is to operate 
is less efficient than reversible 
cycles, and the real engine is ini- 
tially handicapped to that extent. 

(g) The relative efficiency is 




REf 



^ CEf ^ 48 
Efc 92 



Fig. 305. 



52.2 per cent. 



446 HEAT-POWER ENGINEERING 

This shows that the real Otto engine, if absolutely perfect, could 
only make available a little more than half the mechanical energy 
obtainable with the ideal Carnot engine. 

(h) The indicated efficiency measures the amount by which 
the cylinder of the real engine falls short of developing the 
48 per cent of the supplied energy. 

The weight (Wi) of mixture that this engine would probably 
use is about 9 to 10 pounds per i.h.p.-hour, and the heat AQ 
supplied by each pound of mixture is about 940 B.t.u. Then 
the theoretical Otto engine would make available 940 X 0.48 = 
451.2 B.t.u. per pound as AE. One horse power is equivalent 
to 2545 B.t.u. per hour, and the heat theoretically available for 
doing work is (9 or 10) X 451.2 B.t.u.; hence 

lEf = .|^ = , ^ ^\^t 62^6 to 56.4 per cent. 

■' WiAE (9 to 10) X 451.2 ^ t t- 

That is, the area of the upper loop of the real indicator card 
divided by the area of the ideal air card would give a value 
between 62.6 per cent and 56.4 per cent. This measures the 
proportion of the maximum energy of this cycle that is made 
available by the real engine. In Fig. 305, DE should be 62.6 per 
cent to 56.4 per cent of DF. 

(i) The thermal efficiency on the i.h.p. is easily determined to be 

TIEf = ^7^ = , , ^^^{, = 30 to 27 per cent, 

•' WiAQ (9 to 10) X 940 ^ ' ^ 

which shows that the real engine actually converts into mechani- 
cal energy from 30 to 27 per cent of all the heat supplied it. 
Some of this is, however, lost in fluid and mechanical friction, and 
the amount of such loss is measured by the mechanical efficiency. 

The TIEf is the ratio of GH to AC in Fig. 305. 

(j) The mechanical efficiency, MEf, of an engine of this kind 
would probably be about 85 per cent, thus the d.h.p. would be 
about 85 per cent of the i.h.p. In Fig. 305, JK is therefore 85 
per cent of JL. 

(k) The thermal efficiency on the d.h.p. is from Eq. (220) 

TDEf = TIEf X MEf = (27 to 30) X 0.85 = 22.9 to 25.5 per cent, 

showing that the engine actually turns into useful, available 
power about one quarter of all the heat energy supplied it. In 
Fig- 305 the TDEf is given by the ratio of MN to AC. 



INTERNAL-COMBUSTION ENGINES 447 

(1) The over-all efficiency would be by Eq. (221) 

OEf= lEf X MEf = (56.4 to 62.7) X 0.85 = 47.9 to 53.3 per cent, 

showing that the real engine losses (cylinder, fluid friction, and 
mechanical friction) consume about one-half the power which the 
ideal engine with the same cycle would make available. In Fig. 
305 the OEf is the ratio of MN to AB. 

220. Efficiencies of other Commercial Engines, (a) Two- 
stroke-cycle Otto Engines, because of greater cyclinder and 
friction losses, generally have over-all efficiencies of from 0.7 to 
0.8 of those of corresponding four-stroke engines. The indicated 
efficiency and mechanical efficiency may both be lower than 
in four-stroke engines, or the indicated efficiency may be lower 
while the mechanical efficiency is higher because of the absence 
of valves and such. 

(b) The thermal efficiency of the Diesel oil engine is generally 
higher than that of engines working on the Otto cycle. This is 
due to the higher compression pressure which can be carried in 
these engines (500 pounds per square inch or more), and to 
the fact that the combustion conditions are also probably 
somewhat better. 

Average thermal efficiencies on the brake with Diesel engines 
are about 30 per cent, and sometimes run as high as 35 per cent. 

221. Heat Balance for Gas Engines, (a) In reporting an 
engine test, it is customary to account for all heat supplied. The 
statement of this account is called the " heat balance." There 
are only five possible destinations for heat supplied to a gas 
engine. They are: 

(i) Useful mechanical energy; 

(2) Loss to jacket; 

(3) Heat carried away in the exhaust gases; 

(4) Loss due to incomplete combustion; 

(5) Radiation, which includes energy converted into heat by 

friction. 

(b) The useful mechanical work has already been shown to 
equal from 15 to 30 per cent of the heat supplied. 

(c) The relative amount of heat lost to the water, or air, 
jacketing the cylinder varies in different engines, and in the 



448 HEAT-POWER ENGINEERING 

same engine under different conditions. The loss to jacket is 
between 25 and 50 per cent, with an average from 30 to 35 per 
cent. In the case of air jacketing, it is not generally possible to 
distinguish between jacket and radiation losses. 

(d) The loss due to heat carried away by the exhaust gases, 
owing to their high temperature, generally falls between 25 and 
40 per cent, increasing as the jacket loss decreases, and vice versa. 

(e) Combustion is almost always incomplete to a small extent 
and may at times be imperfect enough to account for a consid- 
erable proportion of the heat available. This loss should not be 
greater than i to 2 per cent of the total heat, and is often much 
less. 

(f) Radiation loss is supposed to include all heat radiated from 
the outer surfaces of the engine, and in the heat balance it would 
include all energy converted into heat by friction and subse- 
quently lost by radiation and conduction. It is generally found 
by subtracting the sum of the other four quantities of heat in 
per cent from 100; and when this method is used this difference 
includes all errors of the other results. When calculated in this 
way it may have a value of from 10 to 20 per cent, with an aver- 
age of about 15 per cent. 

(g) Another heat-balance method puts under (i) the energy 
represented by the upper loop of the diagram, instead of the 
mechanical energy delivered. Then the energy loss in gas and 
engine friction is already included under (i) and does not appear 
as radiation loss under (5). The latter value is then reduced 
to about 5 to 8 per cent of the total heat supplied. 

(h) The total heat supplied the engine may be taken as either 
the higher or lower heat value of the gas (see Chapter XXVIII). 
Obviously the use of the lower value results in a higher efficiency 
for the engine, and is therefore favored by gas-engine builders. 
In America the lower value is universally used, although in some 
countries of Europe the higher value is sometimes adopted. 

(i) It is important to note that the thermal efficiencies of 
steam and internal-combustion engines are not strictly compar- 
able unless the amounts of heat available are measured in a 
truly comparable way. This is usually not the case, for the fol- 
lowing reasons: The heat supplied a steam engine is generally 
figured as that in the steam above some datum, such as 32° F., 
or feed-water temperature, or exhaust temperature and is not in 



INTERNAL-COMBUSTION ENGINES 449 

terms of the fuel used or its cost. On the other hand, the heat 
suppHed an internal-combustion engine is based upon a calori- 
metric determination of the fuel, with certain corrections in case 
the lower calorific value is sought. This amounts to figuring the 
heat supplied above a datum equal to the existing atmospheric 
temperature for all the constituents of the exhaust gas excepting 
the water formed by the combustion of hydrogen. The heat value 
of this combustible is figured above a datum which often corre- 
sponds roughly to 212° F. (See Chapter XXVIII for further 
discussion.) 

The datum used is thus arbitrarily chosen for convenience in 
each case, and the results are not strictly comparable. It might 
seem that, since the steam engine is given credit for the heat of 
the liquid in the exhaust steam, or for that part of it above feed- 
water temperature, some sort of similar device might be adopted 
in the case of the internal-combustion engine. This is incorrect, 
however, because the exhaust of the latter engine is absolutely 
useless so far as the engine is concerned. Part of the heat 
carried may be abstracted by generating steam, heating water, 
or in a number of other ways; but this should not affect the 
figure for heat consumption of the engine, although it is properly 
taken account of in determining the efficiency of the plant as a 
whole. 

(j) The only true comparison of heat expenditure is between 
heat-power plants as a whole and not between engines only. 
If the fuel is the same in both- cases, the ratio of the amounts of 
fuel per d.h.p. may be used; otherwise relative economy is shown 
by the ratio of the costs of the respective amounts of fuel con- 
sumed per d.h.p.-hour. 

The true comparison for economic purposes should include 
not only the fuel cost, but expenditure for labor, lubricants, 
supplies, repairs, interest, depreciation, insurance, and all other 
costs involved in power generation ; and only on such a basis are 
two systems truly comparable. 

222. Performance of Internal-Combustion Engines, (a) There 

are so many different kinds of internal-combustion engines that 
it is difficult to make broad statements to fit all cases. The fol- 
lowing must, therefore, be regarded as very general, and appli- 
cable only to the average lines of engines. 



45° 



HEAT-POWER ENGINEERING 



(b) American engines built to run on natural gas are gener- 
ally guaranteed to deliver a brake horse power on from lo to ii 
cubic feet of gas at rated load. This gas is commonly assumed 
to have a calorific value (lower) about looo B.t.u. per cubic 
foot; so this guarantee is from 10,000 to 11,000 B.t.u. per horse- 
power hour at rated load, corresponding to thermal efficiencies 
of from 23 to 25.5 per cent on the d.h.p. Many engines at 
present in operation give better results than these by several 
per cent at rated loads; and the efficiencies are still better at 
loads from 10 to 15% greater than the normal. 

At three-quarter load they are generally guaranteed at 11,000 
to 13,000 B.t.u. ; at half-load, 13,000 to 15,000; and at one-quarter 
load 20,000 to 23,000 B.t.u. 



,1,000,000 




Fraction of Rated Load 
Developed H.P. 



Fig. 306. 



The curves of the total consumption and rate per d.h.p.-hour 
for average 100 horse-power natural-gas engines are given in 
Fig. 306. In each case the two curves correspond to the limits 
above given. The exact shape of these curves will, of course, 
depend upon the type of engine, method of governing, etc., but 
those given may be taken as representing average practice. 

It is convenient to remember that practically all internal- 
combustion engines (with the possible exception of some oil 
engines) will require about twice as many thermal units per horse- 
power hour at one-quarter load as at the rated load. 



INTERNAL-COMBUSTION ENGINES 45 1 

(c) Engines intended to operate on illuminating gas are 
generally guaranteed with lower efficiencies than natural-gas 
engines. The B.t.u. per d.h.p.-hour is usually from 12,000 to 
13,000 B.t.u. at full load. The poorer performance is principally 
due to the fact that these engines are, as a rule, not so carefully 
designed, as they are not built in large sizes or in great numbers 
because of the high cost of this gas. Some of the highest thermal 
efficiencies on record have, however, been obtained with engines, 
using illuminating gas. 

(d) Producer-gas engines are generally guaranteed on a basis 
of coal used per horse-power hour rather than cubic feet of gas 
or B.t.u. The average figure is i to i.i pounds of coal per horse- 
power-hour at rated load, and most producer-gas installations 
of good design can be counted on to produce a d.h.p.-hour on 
less than 1.2 pounds if operated continuously at full load. Under 
accurate test many of them have developed a brake horse-power 
hour on 0.8 to 0.9 of a pound of coal. 

To give an idea of the meaning of these figures, it is sufficient 
to state that a consumption of only 0.8 pound of coal per 
d.h.p.-hour corresponds to a thermal efficiency on the brake for 
the engine alone of about 31 per cent; while i pound corresponds 
to about 25 per cent. 

(e) Gasoline engines (stationary) are generally guaranteed to 
deliver a d.h.p.-hour on one pint of gasoline, at rated load. 
This corresponds to a heat consumption of about 14,000 B.t.u. 
per d.h.p.-hour, or a thermal efficiency of about 18 per cent. 
As a matter of fact, all of the better types are capable of deliver- 
ing a d.h.p.-hour on about two-thirds of the guaranteed quantity, 
when everything is in perfect adjustment. 

Between rated oad and maximum load the efficiency will 
first increase and then due to the use of rich mixture will slowly 
decrease. 

At about one-quarter load the consumption per d.h.p. will 
be about twice that at full load. 

(f) Alcohol engines are not as yet a commercial product in 
this country, and very few figures are available from practice. 
Tests show that such engines can safely be guaranteed on the 
same or a smaller volume consumption than gasoline. It is safe 
to assume a thermal efficiency of 25 per cent on the brake with 
these engines, and figures as high as 32 per cent and more have 



452 



HEAT-POWER ENGINEERING 




7 9 11 13 15 17 19 gl 
B.H.P. and I.H.P. 



Fig. 307. 




ss 00- 

-3 



g20- 
OJ 



SO 

40 
30 


55 H. P. SINGLE CYLINDER 

SINGLE-ACTING HORIZONTAL GAS ENGINE 

USING ILLUMINATING GAS 




^ 


C^J^ 


fiasP. 







— 


/ 




"h 


3> 








/ 


/ 






^ 


3>^ 


■^ 


10 







<^ 


U^ 




Jiiif 


:«... 
















1 


% 


3 


1 


6 


6 


70 



1-10 "^ 



Fig. 309. 



INTERNAL-COMBUSTION ENGINES 

55000 r 
60000 



453 




ii% W' 15% 100^ 125^ 

fc of Rated Load 



Fig. 310. 



.\i^ 



DOUBLE ACTING 
TANDEM HORIZONTAL 
ENGINE OPERATING ON 
BITUMINOUS PRODUCER GAS 




3,000,000 



2,000,000 



.1,000,000 







250 H.P. MARINE TYPE 
DIESEL ENGINE. 




S" 


\ 


\ 








3 




^ 


k 


y 


A 


I 






.<y 


><. 


4 






^ 









D.h.-p.50| 100 I 150 [200 250~ 
5^ Normal Load 25 50 75 100 

Fig. 312. 



13000 
11000 
10000 
9000 



454 HEAT-POWER ENGINEERING 

been obtained. This high efficiency is largely due to the high 
compression pressure that can be used with this fuel. 

(g) Oil engines (kerosene, distillate, and crude) differ widely 
in fuel consumption, but the newer and better American types 
are capable of producing a d.h.p.-hour on from 0.7 to as low as 
0.5 of a pound of oil. These figures correspond roughly to 
thermal efficiencies of from 18 to 28 per cent on the d.h.p. 

(h) The curves given in Figs. 307 to 312 inclusive show results 
of tests of several different types of engines with different fuels. 
They illustrate in a general way how the various efficiencies of 
commercial importance vary with such things as load, size of 
engine, kind of fuel, etc. 



CHAPTER XXVII. 

FUELS. 

223. Fuels, (a) In the discussion of ideal engines in preceding 
chapters, a hot body was assumed to be available and it was 
imagined to be so constituted that it could deliver heat at any 
time and in any desired quantity, with no change in its own 
temperature. No such hot body is really available, and in 
practice supplies of heat are obtained by burning " fuel." 

(b) In the broadest sense fuel is any material which can he made 
to combine with other material in such a way as to liberate heat. In 
the commercial sense, however, fuel is any material the greater 
part of which can be made to combine with oxygen, usually from 
the air, so as to liberate heat, and which is purchasable at such a 
price that its use will yield a profit. 

(c) Fuels may be solid, liquid or gaseous. The principal 
Natural Fuels are Coal, Wood, Petroleum Oil or Crude Oil, and 
Natural Gas. The principal Prepared Fuels are Coke, Briquets 
made from coal. Charcoal, Distillation Products of Petroleum, 
Artificial Gas made from solid or liquid fuel. Hydrogen Gas and 
Acetylene Gas made from noncombustibles, and Alcohol. There 
are also certain kinds of municipal refuse and manufacturing 
wastes which have fuel value. 

224. Geology of Coal, (a) Formation. Beds of coal in the 
different stages of formation are scattered over the earth's sur- 
face. Geologists believe that coal results from collections of 
vegetable matter, deposited in swampy places or under water, 
which are subsequently covered by silt and other material and 
during geological ages are gradually changed in physical and 
chemical composition until they finally become coal. 

(b) Vegetable matter may here be assumed to consist of 
carbon, hydrogen and oxygen combined in definite proportions, 
together with certain incombustible inorganic salts in the cell 
structure. This vegetable matter when under water changes 

4SS 



456 



HEAT-POWER ENGINEERING 



very gradually, losing some of its material in the form of gas 
(usually methane or marsh gas, CHi) and as water. These trans- 
formations continue after the deposit has been deeply covered 
with earth, and eventually only the carbon and the inert salts 
remain. The extent of these changes is principally dependent 
on time, measured in geological ages, on temperature, and on the 
pressure, depth and porosity of the overlying material. 

The combustible part of coal consists principally of volatile 
matter (which is released upon heating to a high temperature in 



OO 90 80 


fo Volatile Matter 
70 60 50 40 30 2 


10 ^ 








\ 


K~ 


K' 


\ 


V 


\ 


s. 


Vegetable 








Matter 








\ 


Li 
B 

B 

A.I 
A 
G 


;Peat 








\ 










^ 










.nite 










\ 










\ 












\ 


f-- 
























\ 














\ 






























tuminous 




























\ 
















\ 


















































\J 


— 
















s 




















SemU 


















tuminouB 


















\ 




















V 


. 




















1"^"':. 








































\ 


IV. 




















\ 


^ 


















, 


, ^ 


aphltio 


1 


a 





3 


i 


5 


6 

ixed 


7 

Carb 


8 

on 


9 


10 




' 



Fig. 313- 



a closed crucible) and of fixed carbon which remains after such 
treatment. As the formation of coal progresses the percentage 
of volatile matter and moisture decreases with corresponding 
increase of fixed carbon. 

(c) Classification. In the early stages of transformation the 
material is called (i) Peat or Turf. Later, with increased pres- 
sure of overlying material resulting in greatly reduced volume, 
it becomes (2) brown or black Lignite. Later still, after addi- 
tional physical and chemical changes, the material becomes 
(3) Soft Coal or Bituminous Coal. Subsequently, it becomes 



FUELS 



457 



successively (4) Semibituminotis, then (5) Semianthracite, (6) 
Anthracite, and finally (7) Graphitic Coal. The last is practically 
pure carbon. These are the seven groups into which coals are 
generally classified.* 

(d) Fig. 313 shows in a very general way the relation of fixed 
carbon to volatile matter during the transformation of vegetable 
matter into coal. 

The horizontal width of the diagram represents the sum of 
fixed carbon and volatile matter. The inclined line divides the 
horizontals into parts which represent fixed carbon (at the left) 
and volatile matter (at the right). Percentages may be read 
from the scales. 

The progress of the transformation is shown by the classi- 
fication at the right of the diagram. This grouping would seem 
to indicate well-defined divisions between adjacent classes; but 
in reality the groups blend into each other. The diagram is 
simply for illustration and should not be used otherwise. 

(e) There is as yet no really satisfactory basis for the classi- 
fication of coal. Formerly the classification was according to 
the percentage of fixed carbon in the dry combustible, as given in 
Table XIII. This, however, is not very satisfactory for coals 
high in volatile matter. 



TABLE XIII. — 


OLD 


CLASSIFICATION OF 


COALS. 


Kind of Coal. 


■ Fixed Carbon. 


Volatile Matter. 


Anthracite 


Per cent. 

97.0 to 92.5 
92.5 to 87.5 
87.5 to 75.0 
75. to 60.0 
65,0 to 50.0 
Under 50.0 


Per cent. 

3.0 to 7.5 

7.5 to 12.5 

12.5 to 25.0 

25.0 to 40.0 

35.0 to 50.0 

Over 50.0 




Semibituminous 

Bituminous, Eastern 


Lignite • 



(f) A recently proposed classification, based on the ratio of 
volatile carbon to total carbon and known as Parr's Classifica- 
tion, f appears to be more satisfactory. Omitting the subgroups 
under bituminous coals and lignites, this classification is given in 
Table XIV. 



* One other group falling between (2) and (3) above and known as " suhhitumi- 
nous " is sometimes recognized. 

t Bull. No. 3 IHinois State Geol. Survey. 



458 HEAT-POWER ENGINEERING 

TABLE XIV. — PARR'S CLASSIFICATION OF COALS. (Abbrev.) 



Kind of Coal. 


Volatile Carbon 
Total Carbon 


Inert Volatile. 


Anthracite 

Semianthracite 

Semibituminous 

Bituminous 

Lignite 


Per cent. 
Below 4 

Between 4 and 8 
Between 10 and 15 
22 to 44 
27 and up 


Per cent. 






5 to 16 
16 to 30 



(g) Coal Fields in the United States.* The main deposits 
in this country are shown in a very general way in Fig. 314, in 
which the average character of each deposit is indicated by the 




FIELDS 
1- R.I. Graphitic 5- Eastern Interior 

2- Pa. Anthracite 6- Western " 

3- Appalachian i-S.W. " 

4-Northern Interior 



Fig. 314- 

kind of hatching. In Rhode Island there is a little graphitic 
coal. Most of the anthracite is found in beds of less than 500 
square miles area located in eastern Pennsylvania. The princi- 
pal deposit of semibituminous coal is about three hundred miles 
long by twenty wide and lies along the eastern edge of the 
Northern Appalachian Field. The bituminous coals extend from 
this deposit westward. Starting with the graphitic coal in 

* See Coal Fields in the U. S. by C. W. Hayes, U. S. Geological Survey, and 
Kent's " Steam Boiler Economy." 



FUELS 459 

Rhode Island, broadly speaking, the farther west a coal is located 
the less advanced it is in the process of transformation. It is 
important to note, however, that there are many exceptions to 
these very general statements, for there are numerous other small 
fields, not shown, scattered over the country. For instance, a 
little anthracite coal is found in Colorado and in New Mexico, 
and some semibituminous in Arkansas. 

225. Composition of Coal, (a) Coals consist principally of 
the elements Carbon, Hydrogen, Sulphur, Oxygen, and Nitrogen, 
together with moisture and ash. The elements named, par- 
ticularly Carbon, Hydrogen and Oxygen, seem to be combined 
in various ways in the solid coal, though little is known of the 
formulas of the compounds in which they exist. The ash contains 
the inert salts of the original vegetable matter, together with silt 
and similar impurities acquired after deposition and submersion. 

(b) ''Moisture " is arbitrarily defined as the material lost when 
a finely powdered sample of the coal is maintained from half an 
hour, to an hour, at a temperature of about 220° Fahr.; or, more 
exactly, as the maximum loss which can be made to occur at 
this temperature. The material driven off in this way is not 
necessarily all moisture, for, with some coals, part of the more 
volatile combustible material may distil off. Moreover, all the 
water content may not be driven off by maintaining the material 
at this temperature. The definition is, therefore, only an arbi- 
trary one, but it seems to be the best that can be devised. 

(c) ''Dry CoaV is coal from which the moisture has been 
driven by heating, as above described. 

(d) " Volatile Matter'' (or " volatile ") is the name given to all 
material driven off when " dry coal " is maintained at a very high 
temperature (between a "red " and "white heat ") in a covered 
crucible (out of contact with air) until there is no further loss of 
weight. This definition is again purely an arbitrary one, but it is 
useful in that it gives a measure of the material which will be 
similarly given off in a furnace or in a coke oven. 

(e) "Fixed Carbon " is defined as the portion remaining after 
subtracting the ash from the material left in a crucible after 
driving off the volatile matter. 

(f) "Combustible " is the term used to designate the part of the 
coal other than moisture and ash. It is, therefore, the sum of 



460 



HEAT-POWER ENGINEERING 



fixed carbon and " volatile," as above defined. It is composed 
principally of carbon and hydrocarbons but it is important to 
note that it also contains noncombustible matter such as Nitro- 
gen and Oxygen and hence the term is a misnomer. When the 
coal contains sulphur a large part of this is also found in the so- 
called combustible. 

226. Coal Analyses, (a) Two types of analysis are in common 
use — one gives what is known as an " Ultimate Analysis," the 
other a " Proximate Analysis." 

(b) In an ultimate analysis of so-called "dry combustible" 
the percentages of Carbon, Hydrogen, Oxygen, Nitrogen, and 
Sulphur are determined. The ultimate analysis of "dry coal" 
also includes the percentage of ash, and in some cases a chemical 
analysis of the ash is also made. Ultimate analyses are seldom 
made by engineers, being more often obtained from chemical 
laboratories. Table XV gives in a general way the approximate 
ranges of the ultimate analyses of the combustible in different 
kinds of coals. More accurate tables of analyses of coals from dif- 
ferent localities can be found in text books on fuels and on boilers, 
in engineer's " pocket books " and in reports and publications 
of the geological surveys of the United States and of various 
states. In consulting such references it is necessary to bear in 
mind that ultimate analyses are sometimes incorrectly made on 
the basis of coal " as received," i.e., on wet coal. In such cases 
the percentages of H and include the hydrogen and oxygen 
of the moisture. 



TABLE XV. — ULTIMATE ANALYSES OF COALS. 







Per Lb. 


of Dry Combustible. 






c 


H 





N 


S 


Anthracite 


92-98 

90. s 

87.3 

75-83 

70-78 

61 


1-3-5 

5 
4-5-5-5 
5-6.8 


2-3 
4-5 
3-4.8 
4-1 1 
10-15 

33 


I 


o-i.S 


Semibituminous 

Bituminous 

Lignite . 


0.9-1.8 

1-2 

2 


0.6-1.3 
0.4-3 
1-3 


Peat. 









(c) The proximate analysis divides the fuel roughly into the 
several parts which have already been described in Section 225, 



FUELS 461 

as Moisture, Volatile Matter, Fixed Carbon, and Ash. While 
this analysis is less exhaustive than an ultimate analysis, it has 
two marked advantages over the latter: (i) It is easily made 
by the engineer and involves the use of very simple apparatus; 
and (2) it indicates, in a general way, the behavior which may 
be expected of the coal during utilization as fuel. 

(d) Proximate analyses are given both on the basis of "dry 
coal " and coal " as received." For purposes of comparison 
with other fuels, the dry-coal basis is the better because the 
conditions of storage and transportation may materially change 
the moisture content. It would be obviously unfair, for instance, 
to charge against a coal, in comparison with others, the fact that 
it had been rained on, or had been stored under water. On the 
other hand, when coal is being purchased by weight, it is as ob- 
viously unfair to pay for water at the price of coal, and there- 
fore for this and similar purposes analyses should be on a basis 
of coal "as received," or else, in addition to the proximate 
analysis of dry coal, there should be a statement of moisture 
content. 

(e) Table XIII gives the approximate range of percentages 
of fixed carbon and volatile in the combustible of the different 
kinds of coal. The proximate analyses of " dry coals " may be 
obtained by introducing average ash contents and altering the 
percentages accordingly. Proximate analyses of coal from 
different localities may be found in the books and reports to 
which reference has already been made. 

(f) It will be shown in later chapters that such data as are 
given by the ultimate analysis can be used for calculating the 
calorific value, and that they are also needed for computing 
losses occurring in furnaces and boilers. For these reasons ulti- 
mate analyses are often desired, even though their actual deter- 
mination is outside the engineer's field. It has been shown by 
Professor L. S. Marks* that, in the case of most coals occurring 
in the United States, the ultimate analysis can be approximated 
from the proximate analysis with sufficient accuracy for deter- 
mining the distribution of boiler and furnace losses and for general 
engineering work. The results which Professor Marks gave by 
curves have been put into the form of equations by Professor 

* Power, vol. 29, p. 928, Dec, 1908. 



462 HEAT-POWER ENGINEERING 

H. Diederichs. Only the principal ones of these equations will 
be given here.* 

Letting V represent the weight-percentage of volatile matter 
in the combustible, then the approximate weight-percentages of 
hydrogen (H), of volatile carbon (C), and of nitrogen (N) are 
respectively 

^ = ^(l^E^- 0-013) (329) 



V + io 
C = 0.02 V^ ) for anthracite and 



o.p (V - 10) ] semianthracite. j .... (330) 

C = o.q{V — 14) for bituminous and semibituminous (331) 

£7 = o.p (F — 75") for lignites. (332) 

N = 0.07 V for anthracite and semianthracite. . . (333) 

.N = 2.10 — 0.012 V for bituminous and lignite. . . (334) 

The occurrence of oxygen and sulphur is apparently more or 
less accidental in character, showing no uniformity, and is not 
expressible by equations. The greater part of all the sulphur 
and some of the oxygen will appear in the proximate analysis 
as volatile, and will therefore be accounted for as hydrogen and 
carbon in the use of these equations. 

227. Fuel Values of Coals, (a) The methods of determining 
the fuel values of combustible materials will be discussed in 
detail in the next chapter; there are a few considerations, how- 
ever, which it is necessary to mention briefly at this point. It 
is customary to state the calorific value of a material in terms of 
the B.t.u. made available by burning one pound. When a 
material containing uncombined hydrogen is burned, this hy- 
drogen unites with the oxygen and forms superheated water 
vapor. If this vapor passes off without surrendering its heat, 
the calorific value of the fuel is less than if that heat is made 
available. Hence the terms lower heat value and higher heat value 
are used to distinguish between the two conditions of combustion. 

(b) As will be explained in Chapter XXVIII, the Calorific 
Value of a coal can be very roughly determined from the ulti- 
mate analysis by the use of Dulong's Formulas. These are given 

* For more complete explanations, percentages of accuracy, etc., see Carpenter 
and Diederichs' " Experimental Engineering," p. 507, and the original article in 
Power referred to in the preceding footnote. 



FUELS 



463 



in Section 243 as Eqs. (376) and (377) and are stated as follows: 

Higher B.t.u. = 14,600 C + 62,000 {H - 0/8) + 4000 S. 
Lower B.t.u. = 14,600 C + j2,ooo (H — 0/8) + 4000 S. 

If for C, H, 0, and 5 are substituted the weights of these elements 
per pound of combustible, the results will be B.t.u. per pound of 
combustible. If weights per pound of dry coal are used, the 
result will, of course, be B.t.u. per pound of dry coal. 

As will be explained more in detail in the next chapter, Du- 
long's formulas are only approximate because they assume all 
the oxygen originally present in the fuel to be combined with 




rixLd Cdi bon la. the Combustible 



Fig. 315- 

hydrogen, and because they take no account of the disappear- 
ance of heat accompanying the dissociation of hydrocarbons 
and similar obscure phenomena occurring during combustion. 
For accurate determination of the calorific value, some form of 
ftiel calorimeter should be used. These calorimeters will be dis- 
cussed in Section 244. 

(c) Various empirical formulas have been proposed for giving 
the heat value per pound of fuel in terms of the proximate 
analysis. These usually contain "constants," which are given in 
tables, and which vary with the locality of the mine, or with the 
ratio of certain constituents, such as volatile matter to total com- 
bustible. These formulas will not be given in this brief treatment. 

(d) Fig. 315 gives Mahler's Curve,* which shows in a general 

* Redrawn from curve given in U. S. Geol. Survey Professional Paper No. 48. 



464 HEAT-POWER ENGINEERING 

way how the heat value per pound of combustible varies with the 
percentage of fixed carbon present, and which also shows the 
range of percentages of the fixed carbon in the different kinds of 
coal as they are usually classified. This curve shows clearly that 
of all coals the semibituminous has the combustible of the highest 
heat value; and in connection with the map in Fig. 314, it is seen 
that in general the coals are of decreasing heat value the farther 
they are located from the main semibituminous bed. It is also 
true, generally, that the difficulty encountered in burning a coal 
efficiently increases with the distance of the mine from this same 
bed. 

(e) Coal when mined always contains moisture and often takes 
up more afterward. Moisture is generally undesirable because 
it is not combustible and because it is vaporized and superheated 
during combustion, thus absorbing heat that might otherwise be 
utilized. Eastern coals, as mined, contain from one to five per 
cent of moisture, western coals from three to fifteen per cent, and 
lignites from ten to thirty per cent. 

(f) Ash not only decreases the heat value of fuel, but it also 
increases the cost of transportation and handling of the coal per 
unit of heat produced, and in addition there is the cost of its 
disposal after combustion. The presence of ash also interferes 
with combustion, especially if it is of such composition as to 
form clinker. The percentage of ash in commercial coals ranges 
from three to fifteen ordinarily, and is usually greater in the 
smaller sizes than in the larger. 

(g) Sulphur, although combustible, usually makes the fuel un- 
suitable for use under boilers and for many other purposes, if 
present in large quantities. The products of its combustion 
may, under certain circumstances, form acids by combining with 
water and these may attack the metal of boilers, etc. The pres- 
ence of considerable quantities of sulphur is supposed to indicate 
a readily fusible ash which causes trouble in the boiler furnace, 
or in the " gas producer," by the formation of clinker. 

(h) Peat, in its natural state, is a poor fuel containing a large 
percentage of moisture. Its value is improved by drying, but it 
is not yet generally used when other cheap fuels can be obtained.* 

* As an indication of what may be expected when other fuels become scarcer, 
see Bulletin 16, U. S. Bureau of Mines, " The Use of Peat for Fuel and Other 
Purposes." 



FUELS 



465 



(i) Lignite is an unsatisfactory fuel when burned in furnaces, 
but recent investigations seem to indicate that it may be of great 
value for the making of " producer gas " for which there is a 
rapidly growing demand for power purposes. 

(j) Western bituminous coals are a little harder to burn efifi- 
ciently than eastern on account of the larger proportion of volatile 
matter contained. The higher the percentage of volatile matter 
in the coal the more difficult it is to burn it smokelessly and 
efficiently (see Chapter XXIX). 

(k) Bituminous coals are sometimes classified as caking and 
noncaking. The fragments of the former kind coalesce into cakes 
while burning, which is desirable in the making of coke but may 
interfere with the supplying of air for combustion when the coal is 
burned upon grates. 

(1) Cannel coals are bituminous coals which are very rich in 
hydrocarbons and burn like a candle, hence the name. These 
are used as " enrichers " in gas making. 

Coals high in hydrocarbons burn with a long flame and are 
more difficult to burn efficiently than short-flame coals. 

(m) Semibituminous coals, as has been shown, have the highest 
heat value per pound, and, as they burn with a comparatively 
short flame, they are the most desirable coals for use in boiler 
and similar furnaces. 



TABLE XVI. — COMMERCIAL SIZES OF SOFT COAL. 



Lump. 

Nut. . 
Slack. 



Through Bars 
Spaced Apart. 



Over Bars Spaced 
Apart. 



(n) Anthracite coal has an advantage over the other classes 
in burning smokelessly, and consequently is in great demand 
where smoke is not permitted. The available supply in the 
eastern part of the United States is rapidly diminishing and the 
price is, in general, higher than for other coals. To obtain the best 
results with anthracite it must be of uniform size. As the price 
decreases with the size, only the smaller grades, usually those less 
than I" in diameter, are used for power purposes. Table XVII 
gives the usual classification, but unfortunately the names and 
sizes in some instances vary with the locality. 



466 



HEAT-POWER ENGINEERING 
TABLE XVII. — SIZES OF ANTHRACITE COAL. 



Name. 


Through Screen 
with Mesh. 


Over Screen 
with Mesh. 






2| 
2 

1 

I 

1 

Unscreened 


Egg 

Pea 

Buckwheat No. i. 
Buckwheat No. 2. 
Run of mine 


2| 
1 

Unscreened 



(0) Coal dust, produced in mining the material, is almost 
always a waste product. Such dust is now successfully used in 
firing rotary kilns and similar apparatus, but is seldom used for 
ordinary power purposes although special devices for burning 
it under boilers and in producers have been used to a limited 
extent. 

Coal dust and similar waste, known collectively as " culm " 
may represent from 10 per cent to as high as 50 per cent of all 
the coal recovered from the mine. It is, therefore, apparent 
that sooner or later some method of utilizing this waste will 
have to be adopted because of the decrease in the available supply 
of coal. Such material has been very successfully recovered in 
Europe by forming it under high pressure into briquets in which 
such materials as pitch, resins, wax tailings, starch, and several 
inorganic salts are used for " binders." These -briquets can 
often be used more efficiently than ordinary lump fuel, because 
of their uniformity of size, advantageous shape, and general good 
behavior in the furnace; hence it often proves to be economical 
to purchase briquets at a slightly higher price than that asked 
for similar lump coal.f 

228. Coke is the solid material left after driving off the 
volatile part of coal by heating with total or partial exclusion of 
air. Only certain coals yield coke of commercial value. Nearly 
all of the coke made is used in metallurgical processes, and but 
little as yet for power purposes. 

* There are a number of other sizes, such as " stove," " chestnut," etc., which 
need not be considered here as they are not commonly used in heat-power 
engineering. 

t For investigations relating to the manufacture and utilization of briquets 
under American conditions see bulletins of the U. S. Geol. Survey and of the U. S. 
Bureau of Mines. 



FUELS 467 

Coke contains from 80 to 93 per cent of fixed carbon, from 5 to 
18 per cent of ash, from 0.5 to 1.5 per cent of sulphur, and traces 
of volatile. It is interesting to note that the volatile is not 
entirely eliminated, and that, as all the ash in the coal remains in 
the coke, the percentage of inert matter present' in the product 
must be greater than that in the original material. 

The calorific value per pound of combustible is about the same 
as for carbon; that is, it is in the neighborhood of 14,600 B.t.u. 

229. Wood, (a) As wood is about half moisture when felled, 
it must be dried before it is of much value as fuel. Air-dried wood 
generally has from 15 to 20 per cent of moisture, about 50 per 
cent of carbon, from j to 2 per cent of ash, and the rest is 
volatile matter, largely inert. The heat value per pound of dry 
material is from 6600 to 9800 B.t.u. 

When other cheap fuel is available wood is not generally used 
for power production. However, refuse from sawmills and other 
wood-working factories may be profitably utilized. 

(b) Charcoal is made from wood in much the same manner 
that coke is made from coal. It is ordinarily used in power 
plants only when it is the by-product of some local process, such 
as the manufacture of turpentine or wood alcohol. It may con- 
tain from 80 to 97 per cent of carbon, depending on the tempera- 
ture and treatment used in carbonizing it. 

230. Municipal and Industrial Waste. In cities and indus- 
trial centers there is a constant accumulation of combustible 
waste and in some cases this material is burned directly as fuel, 
or it is gasified in suitable apparatus and the resultant combustible 
gas used as fuel. Installations of this character are still rare but 
are of growing commercial importance. 

231. Natural Oil and Its Products, (a) Petroleum, or Crude 
Oil, has come into extensive use as fuel in the last twenty-five 
years. It is a more or less viscous, dark brown or greenish 
colored liquid occurring in natural reservoirs in the earth's crust. 
These reservoirs may be subterranean pockets, but are, in general, 
oil-saturated strata buried beneath other strata which are prac- 
tically impervious to petroleum. 

(b) Petroleum in its crude form generally has a specific gravity 
between 0.82 and 0.92. It is a mixture of various hydrocarbons 



468 HEAT-POWER ENGINEERING 

which are liquid at ordinary temperatures and pressures, and 
which hold in solution numbers of other hydrocarbons which 
otherwise would be gaseous or solid under existing conditions. 
In general, oils from one field are composed of the same hydro- 
carbons in about the same proportions, but each field has its own 
characteristic composition. American crude oils have from 82 
to 87 per cent of carbon, from 12 to 15 per cent of hydrogen, and 
from o to 4 per cent of oxygen in their composition. The lower 
heat value per pound of crude petroleum varies from 18,000 to 
22,000 B.t.u. 

(c) Many of the more highly inflammable volatile components 
tend to distill off when the oil is brought to the earth's surface 
and is exposed to atmospheric conditions. These volatiies, some 
of which boil at temperatures as low as 80° F., are usually dis- 
tilled off progressively in a refinery. The distillation products 
most commonly used as fuels are naphtha, gasoline, kerosene, and 
distillate, given in order of decreasing inflammability and increas- 
ing density and distillation temperature. The greater part of the 
remainder can be sold as " fuel oil." 

(d) Gasoline is the name given to the group of hydrocarbons 
which distill off at temperatures between 150 and 300° F. Gaso- 
lines of various specific gravities are obtained by fractionating 
the material obtained between these temperatures, the lower 
gravities corresponding to the lower temperatures. The com- 
monest grades range from 74 to 64 degrees gasoline as measured 
by a Baume hydrometer. The corresponding specific gravities 
are 0.686 and 0.722. The relative proportions of carbon and 
hydrogen in gasolines are roughly 85 per cent and 15 per cent, 
and the lower calorific value is about 19,200 B.t.u. per pound. 
The flash point of gasoline, that is, the temperature at which 
readily inflammable vapors are given off from an exposed surface, 
is generally well below 70° F. 

(e) Kerosene is the name of the next important group of 
hydrocarbons which distill over after the gasolines. Their 
specific gravity is from 0.78 to 0.82 and the flash point is from 
70° to about 150° F. for the different grades. The B.t.u. per 
pound of kerosene is about 18,500 lower value. 

(f) Fuel Oil, having little highly volatile matter, can be handled 
without danger and, being very cheap, is quite widely used under 
boilers and in furnaces. The lower calorific value per pound is 



FUELS 469 

extremely variable, but may be taken roughly at 18,000 B.t.u. 
per pound. 

(g) The higher calorific value of U. S. petroleum and its dis- 
tillates, ranging from crude oil to gasoline, varies quite regularly 
with the specific gravity of the material, and is expressed ap- 
proximately by the following formula,* which may be assumed 
correct within 2 per cent, 

B.t.u. per pound = 18,650 -]- 40 (5 — 10), . . (335) 

in which B = degrees on the Baume hydrometer. Since the 
Baume scale increases as the density of the material becomes 
less, this formula indicates that the lighter distillates have 
greater heat values than the heavier ones, when figured on a 
weight basis. The reverse is true for heat value per gallon, a 
unit commonly used with liquid fuels; hence a barrel of light 
petroleum distillates of any kind will, in general, have less heat 
value than a barrel of heavier distillates or of the original oil 
free from water. 

232. Alcohol, (a) Both Methyl (" Wood ") and Ethyl 
(" Grain ") alcohol are used as fuel to a limited extent. Methyl 
alcohol (CHiO) is poisonous and is produced during the dry dis- 
tillation of wood. Ethyl alcohol (CiHeO) is made, by a fermen- 
tation and distillation process, from grain, fruit, or vegetable 
matter containing starch or sligar. 

(b) The material known as Denatured Alcohol consists of ethyl 
alcohol with the addition of from i to 10 per cent of Methyl 
alcohol and other substances which prevent its use in beverages 
and give it an unpleasant odor. Commercial alcohol generally 
also contains 10 per cent or more of water by volume. 

Denatured alcohol has many theoretical and practical advan- 
tages over gasoline as a fuel for certain purposes, but at present 
its relative cost, in this country at least, is so great as to prevent 
its extensive use. 

(c) The higher calorific value of Absolute Ethyl alcohol (i.e. 
containing no water) is about 13,000 B.t.u. /lb.; the lower value 
is about 12,000 B.t.u. /lb. The heat value of " Commercial " 
alcohol, containing about 10 per cent of water, by volume, varies 
with the materials used in denaturizing. The lower heat value 
is generally near 10,500 B.t.u. /lb. 

* H. C. Sherman and A. H. Kropff, Jour. Am. Chem. Soc, Oct., 1908. 



470 



HEAT-POWER ENGINEERING 



233. Natural Gas. (a) This material is found in various 
places, but particularly in certain regions of the United States, 
either escaping through cracks and faults in the earth's crust, 
or held at high pressure in huge underground reservoirs which 
may be tapped by drilling wells similar to those used for ob- 
taining oil; in fact, most oil wells yield a certain amount of 
natural gas. 

(b) Natural gas is a mixture of combustible and incombustible 
gases, the latter generally occurring in very small quantities. 
The proportions and even the constituents of the gas are seldom 
the same in different districts and occasionally vary unaccount- 
ably even in the same well. 

The principal combustible constituents are Methane (CH4), and 
Hydrogen ( H2) . The former generally occurs in far greater pro- 
portion than the latter. The other combustible gases which 
usually occur in very small proportions are Carbon Monoxide, 
(CO), sulphur compounds such as Hydrogen Sulphide {H2S), and 
certain hydrocarbon gases, such as Ethylene (CzHi), and others. 

The principal incombustible constituents are generally small 
proportions of Carbon Dioxide (CO2), Nitrogen (N2), and Oxy- 
gen (O2), if this latter may be considered an incombustible. 

(c) Natural gas is an ideal form of fuel for many industrial 
purposes, and is readily piped distances of one hundred miles and 
more for use in industrial centers far from a natural supply. 
Unfortunately many of the wells are becoming exhausted and 
the price is rising in proportion. 



TABLE XVIII.* — TYPICAL ANALYSES 


OF 


NATURAL GAS. 




Analyses in Volumes, Per Cent. 


Location of Field. 


1*' 




i 


1^ 
.S i 

go 


11^ 


1 





1^ 


i 




1. 86 
1. 31 


93.07 
87.7s 
96.50 
92.60 
80.11 
96.34 
72.18 
77.03 
92.49 


0.47 




0.26 
6.60 

0.26 
0.66 
3.64 
0.80 
3.60 
0.93 


0.73 


0.42 


3.02 
4.34 


0.15 




Olean, N. Y 


5. 72 


I.OO 

0.31 

trace 
6.30 
4.80 
4. II 


0.50 
0.50 


2.00 
0.34 




Findlay Ohio 


2.18 
13.50 


3.61 




Harvey Well, Pa 














Pittsburgh Pa 


20.02 


I.OO 

3.50 


0.80 
1.80 








8.90 
2.13 






0.34 













Abstracted from Table in "Calorific Value of Fuels," Herman Poole, p. 241. 



FUELS 471 

Table XVIII gives some typical analyses of natural gas from 
several different districts. The lower calorific value generally 
varies from about 950 to 1000 B.t.u. per cubic foot. 

234. Artificial Gases, (a) The principal artificial gases are 
made from coal or crude oil, but there are also many processes 
for producing combustible gases from vegetable and animal by- 
products and wastes. Many of the latter are successful in iso- 
lated cases but they are not yet of great commercial importance. 

(b) Most of the artificial gases are made either by destructive 
distillation, by partial combustion, by chemical decomposition, 
or by various combinations of these processes. 

Destructive distillation occurs when the gas-making material 
is heated in a chamber from which air is more or less perfectly 
excluded. Illustrations of gases made by this process are 
" Illuminating," " Retort," or " Town Gas," used for illumi- 
nation, and gas made in " By-product " or " Retort Coke 
Ovens " used for illumination and power. 

" Producer Gases " are the best examples of those which in 
theory are made by a process of incomplete combustion. Practi- 
cally this is always more or less combined with chemical de- 
composition. These gases have become so important of late 
in connection with the internal combustion engine that they 
will be discussed later in a separate chapter. 

(c) The use of artificial gases as fuel in internal combustion 
engines results generally in a greater output of available energy 
than would the use of the solid fuels, from which the gases are 
made, in other heat-power apparatus ; hence these gases may be 
expected to become more and more important with the depletion 
of the natural stores of fuel and with the growth of the spirit of 
conservation of the earth's resources. 



CHAPTER XXVIII. 
COMBUSTION. 

235. Definitions, (a) To the engineer Combustion means the 
chemical combination of certain elements with oxygen at such a 
rate as to cause an appreciable rise of temperature. 

Practically all chemical reactions are accompanied by libera- 
tion or absorption of heat. When heat is liberated the reaction 
is called exothermic; when heat is absorbed the reaction is 
called endothermic. 

(b) During these reactions, with other conditions constant, 
(i) the amount of heat energy liberated or absorbed is independ- 
ent of the time occupied; and (2) for any material taking part 
in the reaction, the heat change is directly proportional to the 
mass of that material. 

(c) Materials which can be caused to unite with oxygen to 
produce heat are known as Combustibles. For engineering pur- 
poses they are limited to Carbon and Hydrogen; these, either 
pure or in various combinations, constitute practically the entire 
stock of available combustibles, although a trace of sulphur 
usually appears as an impurity. 

(d) In heat-power engineering the object of combustion is 
either the production of heat directly, or the formation of a more 
suitable kind of combustible, such as gas or coke, from the 
original material. 

Useful combustion data are given in Table XIX. In it the 
values of specific densities and volumes are given for an average 
atmospheric temperature of 62° F. as well as for 32° F. 

236, Combustion of Carbon, (a) Carbon is the principal com- 
bustible in nearly all engineering fuels. This element combines 
with oxygen to form two oxides, — Carbon monoxide {CO), and 
Carbon dioxide (CO2). If CO is formed, the combustion is said 
to be " incomplete " ; if COi is formed, it is said to be " complete " 
or " perfect." 

472 



COMBUSTION 



473 



1 
1 

$ 

Q 
§ 

1 


Is 

^i2 


?l 






o o o o o 

It 1 1 s 








1^ 






It II i 








I|5 






8 1 § § § 8 

5? IP 3 








1 


3 oj V 






\0 M H 








& 






00 O vO t^ ^ 








|o5 






M oi 00 IH d 








1^^ 
1°^^ 






88" §S 8 








is 


U 


6 6 




d d 


On 

d 


U 


lO 00 

d 


O 
CO 


1 1 

d d 


d 


1^ 


5 5r 




<> 

CO 


ro 00 


°° 




w C« 


o 

00 


00 O 

H 00 




i 




O »o 

o o 


ON 

d 


CO NO 

d d 


O 




1 1 

o o 


00 




oo |^^ 

d d 


oo 

CO 

d 




^0■*IN H(N 00-+00 Tj- 


Is 


o^o tqco 88tq ^ 








> 
C 


2 


o: 


M I- 

II 
K <7. 


§§§1 


t 
1 


¥ 





474 HEAT-POWER ENGINEERING 

(b) The reactions occurring during combustion may be ex- 
pressed by chemical equations, the symbols used standing for 
definite proportions by mass or weight. For engineering pur- 
poses the atomic weight of Carbon may be taken as 12, that of 
Nitrogen as 14, and that of Oxygen as 16. 

(c) When carbon and oxygen combine to form Carbon Dioxide 
the reaction is expressed by 

c + 02 = 002; (336) 

the weights combined are 

12 of C + (2 X 16) of = 44 of CO2, 
and dividing this by 12 gives 

lof C + 2|of = 3|of COa. ... (337) 
Thus if 1 pound of carbon unites with 2f pounds of the result 
is 3f pounds of CO2. It is also found that heat equal to about 
14,600 B.t.u. is liberated per pound of carbon when this reaction 
occurs. 

(d) When carbon is burned to Carbon Monoxide, the reaction 
is expressed by 

2 0-^02 = 2 CO; (338) 

the weights combined are 

(2 X 12) of C + (2 X 16) of = 56 of CO, 
and dividing this by 24 gives 

lof C -Ml of = 2i of CO. . . . (339) 
The heat liberated is, in this case, about 4500 B.t.u. per pound 
of carbon. 

(e) The gaseous CO formed as above can be burned to CO2. 
The reaction is 

2 00 + 02 = 2 CO2; (340) 

the weights combined are 

\2 X (12 -f i6)| of CO -f- (2X 16) of = 88 of CO2, 
and dividing this by 24 gives 

2i of CO + i| of = 3f of CO2. . . . (341) 
Thus the 2\ pounds of CO, which would result from the com- 
bination of 1 pound of carbon as in Eq. (339), would combine 
with i\ pounds of to form 3! pounds of CO2. 

This reaction is accompanied by the liberation of heat equal to 
about 10,100 B.t.u. per pound of carbon. Therefore the heat 



COMBUSTION 475 

liberated per pound of carbon monoxide ^as must be 10100/2^ = 
4300 B.t.u. 

The specific volume of CO is 12.81 cu. ft. at 32° F. and 14.7 
pounds pressure. Hence the heat liberated per cu. ft. of CO under 
these conditions is 4300 -7- 12.81 = 335 B.t.u. As CO is a con- 
stituent of many commercial fuel gases and as these are usually 
measured volumetrically instead of gravimetrically, this value 
is convenient for determining the heat available due to the CO 
present. 

(f) Equations expressing both the reaction and the libera- 
tion of heat per pound of material * may be written as follows : 

C -f O2 = COi + (14,600 B.t.u. per pound C) . . (342) 
2 C + 0-2 = 2 CO -{- (4500 B.t.u. per pound C) . . (343) 

2 CO + O, = 2 CO. + i (/°.'«° Bt"- ?«■■ P°™d O (344) 
I or (4300 B.t.u. per pound CO) (345) 

Noting that 4500 + 10,100 = 14,600, it is evident from these 
equations that when carbon is burned to CO2, the ultimate 
results are the same whether the process takes place in one or 
in two steps. 

Further, if part of the pound of carbon (say Cx pounds) is 
burned to CO 2 and the rest {Cy pounds) to CO, the heat liberated 
is 

B.t.u. = 14,600 Cx +4500 Cy. . . . (346) 

(g) If heat is the object of combustion, the carbon should of 
course be burned to carbon dioxide rather than to carbon mon- 
oxide. If CO is formed instead of CO2, the proportion of the heat 
lost is (10,100/14,600) = .69 -|-, or about 70 per cent. If, how- 
ever, the CO is burned later, the rest of the heat may be recovered. 

* As will be seen later, it is sometimes more convenient to modify Equation (342) 
so that the heat quantity as well as symbol C will correspond to 12 lbs. of carbon 
(the pounds being taken as numerically equal to the molecular weight of C involved) . 
The equation then becomes 

C + O2 = CO2 + 175,200 (342a) 

where 175,200 = 12 X 14,600. 

Similarly, for the 24 lbs. of carbon represented by 2 C and by 2 CO, Eqs. (343) 
and (344) become 

2 C + O2 = 2 CO + 108,000 (343a) 

and 2 CO + O2 = 2 CO2 + 242,400 (344a) 

in which 108,000 = 24 X 4500, and 242,400 = 24 X 10,100, 



476 HEAT-POWER ENGINEERING 

When there is less than enough oxygen to burn the carbon to 
carbon dioxide, both CO2 and CO will be formed and the relative 
amounts of each can be determined in the following manner: 
Assume first that there is 1 per cent deficiency in the oxygen 
supply needed to form CO2 and that in consequence 99 per cent 
of the carbon is burned to CO2 and 1 per cent remains C; then 
assume that this 1 per cent of C combines with some of the CO2 
according to the equation C + CO2 = 2 CO; thus it is seen that 
there is finally 2 per cent of the carbon present in CO and 98 per 
cent in CO2.* In general, then, if there is y per cent deficiency 
of oxygen there will be 2y per cent of the carbon burned to 
carbon monoxide instead of to CO^. Hence from the preceding 
paragraph it follows that with y per cent deficiency of oxygen 
there is (2 X .7) y per cent, or 1.4 3' per cent less heat developed 
than if all the carbon were burned to CO2. The great importance 
of having a sufficient supply of oxygen is thus apparent. 

The discussion in the preceding paragraph presupposes that 
the oxygen supply is at least sufficient to burn all the carbon to 
CO, — that is, that the deficiency is not more than 50 per cent 
on a basis of combustion to CO2. Should y be greater than 50 
per cent, some of the carbon will not be burned at all. The per- 
centage not affected will he 2 (y — 50) . 

(h) It is sometimes possible to reverse chemical reactions, — 
in the present case, for instance, to break up one of the oxides 
into the original elements. When this is done the same amount 
of heat will be absorbed during the decomposition as was origi- 
nally liberated during combination. 

Thus, if it is possible to break up the quantity of CO2 con- 
taining a pound of carbon into the elements C and O, it will 
require an expenditure of 14,600 B.t.u. Similarly, it will require 
10,100 B.t.u. to reduce to the monoxide CO an amount of CO2 
containing one pound of carbon, and 4500 B.t.u. per pound of 
carbon will be consumed in separating CO into its elements. 

237. Weights of Oxygen and Air Necessary for Combustion 
of Carbon. It was shown that for each pound of carbon burned 
to CO2 there are required 2f pounds of oxygen, or i^ pound of 

* These statements should be limited to take account of certain " equilibrium " 
conditions which will be discussed in a later chapter. For the present purpose, 
however, they are sufficiently exact. 



COMBUSTION 



477 



if CO is formed. If, as before, Cx and Cy are the weights of 
carbon burned respectively to COi and to CO, then the number 
of pounds of oxygen used are 

Pounds of = 2f C^ + li Cy. ... (347) 







TABLE 


XX.- 


-PROPERTIES OF AIR 










Relative Propor- 
tions. 


Ratio of Air 
too. 


Ratio of A^ 
too. 


Spec. Wt. 

at Atm. 

Pres. 


Spec. Vol. 

at Atm. 

Pres. 




Exact. 


Approx. 


Exact. 


Approx. 


Exact. 


Approx. 


32° 


62° 


32° 


62° 


By 

Weights. 


{0.766 AT 
( 0.234 

So 791 N 
(0.209 


0.77 iV 
0.23 

0.79 AT 
0.21 


4.27 
4.78 


4.3s 
4.76 


327 

378 


3 35 

376 


0.0S072 


0.07609 


12.39 


13-14 


By 


Specific Heats. 


Volumes. 


Cp=o.238 C»=o.i69 



Since, in ordinary engineering work, pure oxygen cannot, in 
general, be conveniently obtained, it is customary to utilize the 
oxygen of the atmosphere. Table XX shows that air is composed 
by weight of about 23 parts of oxygen and 77 of nitrogen; * thus 
the ratio of air to the oxygen it contains is about 100/23= 4.35, 
and of nitrogen to oxygen is about 77/23 = 3.35. Hence, for each 
pound of oxygen supplied there must be used 4.35 pounds of air 
containing 3.35 pounds of inert nitrogen. An equation for 
finding the weight of air required to burn Cx pounds of carbon 
to COi and Cy pounds to CO can therefore be found by multi- 
plying both sides of Eq. (347) by 4.35. This gives (approxi- 
mately) f 

Pounds of Air = 11.6 C + 5.8 C^,. . . . (348) 

238. Volumes of Gases Involved in Combustion of Carbon. 

(a) The combustion formulas, like other chemical formulas 
involving gases, can be read in terms of molecules and of volumes 
as well as in terms of weights. Thus 

2 C + 02 = 2 CO 

may be read, " two atoms of carbon unite with one molecule of 
oxygen to form two molecules of carbon monoxide." But accord- 

* This is the common engineering assumption. Atmospheric air always 
contains carbon dioxide and water vapor as well as a few rare gases such as argon. 

t The quantity 11.6 (often taken as 12), representing the weight of air required 
for complete combustion of one pound of C, will be frequently used by the student 
hereafter; hence it should be remembered. 



478 HEAT-POWER ENGINEERING 

ing to Avogadro's law the same number of molecules are con- 
tained in equal volumes of all the different gases when at the 
same temperature and pressure. Therefore, since every molecule 
of oxygen in a given volume of gas is capable of yielding two 
molecules of carbon monoxide, it follows that one volume of 
oxygen will yield two volumes of CO, both being measured at the 
same temperature and pressure. 
Similarly the equation 

C + O2 = CO2 
shows that one volume of oxygen yields one volume of carbon 
dioxide; and the equation 

2 CO + 02 = 2 CO2 

shows that two volumes of carbon monoxide combine with one 
volume of oxygen to form only two volumes of carbon dioxide. 

(b) In the first case cited there was an increase of gas volume, 
in the second there was no change, and in the third there was a 
diminution. If the gases appear in terms of molecules (O2, N2, 
H2, CO, etc.) in the chemical equations, the coefficients of the 
molecule symbols represent relative volumes. 

(c) Since air is composed of about 21 parts of oxygen and 

79 parts of nitrogen by volume, every volume of atmospheric 

79 
oxygen will carry with it-^ = 3.76 volumes of nitrogen. 

When air is used to support combustion the nitrogen takes no 
chemical part in the reactions considered but simply mixes with 
the products of the combustion and is known as a diluent.* 

A simple relation can now be shown : Since the volume of 
CO2 formed by combustion of carbon equals the volume of the 
oxygen used in the process and since oxygen forms 21 parts of 
air by volume, it follows that with " complete " combustion the 
products will consist of 21 parts CO2 and 79 parts N by volume 
when not diluted by the presence of excess air. 

(d) Then if the carbon is burned in air and if analysis of the 
" flue " gas shows that the volume of CO2 is less than 21 per cent, 
it follows that either (1) there is more air present than is required 
for complete combustion, the excess acting as a diluent, or (2) 
that there is a deficiency of air, with the result that only a part 

* Under some conditions part of the nitrogen burns to an oxide, but the quantity 
thus consumed is small in all the ordinary engineering processes. 



COMBUSTION 



479 



of the carbon is burned to CO-i, the rest appearing in CO. If the 

percentage of COi is less than 21 and no CO is found in the flue 

gas it indicates that there is excess air; and if CO is present 

there is a deficiency.* 

(e) The percentage of CO2 by volume in the flue gas mixture 

can be computed for any condition of combustion, by using the 

following formula, 

D ^ r /-/I 1 1 vol. of CO2 

Per cent of 00-2 by vol. 



wV 



(wV) + (wV)i +etc. 



X 100 



total vol. of gas 

wY 



X 100 



S {wY)n 



X 100, 



(349) 



in which w = weight of CO 2 present in the mixture, 

Wi, W2, etc. = weights of the other gases present, 

V = specific volume of CO2, 
Vi, V2, etc. = specific volumes of the other gases. 

The specific volumes of gases are given in Table XIX. 

(f) If an excess of air is supplied, say x per cent more than is 
required for perfect combustion, the maximum per cent of CO 2. 
by volume which could be present in the flue gas can be computed 
in the following manner, based on the combustion of one pound 
of carbon. In this case the combustion of the pound of carbon 
will result in 3I pounds of CO2; it will theoretically require 11.6 
pounds of air; there will be 0.77 X 11.6 = 8.9 pounds of nitrogen 
accompanying the oxygen used for combustion ; and there will 

be ( 1 1 .6 X ) pounds of excess air. The following table gives the 

weights {w) of gas present per pound of C burned to CO2, their 
specific volumes (V) at 62° F., and the products of these quan- 
tities (wV). 

TABLE XXI. — FLUE GAS CONSTANTS. 



Gas. 


w 


V62 


wV 


CO, 


3f 


8.62 


31.6 


N^^^e^^r, 


8.9 


13.60 


121. 


Air 


II .6 X 
100 


13-14 


1.52 X 



* These statements should be limited to take account of certain " equilibrium " 
conditions discussed in a later chapter. For the present purpose, however, they 
are sufficiently exact. 



48o 



HEAT-POWER ENGINEERING 



The sum of the last column is, 

S (wY)n = 31.6 + 121. o + 1.52 X = 152.6 + 1.52 iC 



153(1 +— 1, approx. 



Then from Eq. (349) 
Per cent CO2 by vol. 



31.6 



'53|1 + ™ 



X 100, approx., (350) 



which gives the proportion of CO2 in the flue gas. 

(g) Again, since the per cent of CO2 by volume decreases 
directly as the quantity of total air is increased, it is evident from 
(c) that 

Per cent CO-2 by volume = 21 -=- (l + :x;/ioo), . (351) 

in which x, as before, represents percentage of excess air. Sim- 
plifying Eq. (350) results in the same equation (approximately). 
The relation of the CO2 to x is shown in Fig. 316 by the curve to 
the right of oO. 



35- 

30 

s 

8 15 























\ 






















\ 

\ 
























V'o 
























^ 


^ 


^ 


\ 
















^ 








V 










8^" 
•^ 5 






/°' 




\ 








4 






__ 


/ 




_ 




\ 
\ 















f ^Deficiency 



100 160 200 850 300 

X foi 



Fig. 316. 



(h) The expression (l + x/ioo) is known as the excess 
coefficient X. In words, — the excess coefficient is the number 
by which the theoretical amount of oxygen, or air, required must 
be multiplied to find that actually supplied. 

If the CO2 percentage is known, and if the combustion is 
complete (and only in that case) the per cent of excess air x, 
can be found from Eq. (351). Thus 
21 



( ££ A 

\per cent 00% ) 



^percent CO. ' l"'°- ' ' ' ' ^^S^' 
(i) For the case of complete combustion, the percentage of 



COMBUSTION 



4S1 



excess air can also be found when both the total volume {N) of 
nitrogen and the volume {Ox) of that part of the oxygen which 
remains free after combustion are known. The volume of 
nitrogen accompanying the excess oxygen is 79/21 X 0^ = 3.76 Ox, 
and that corresponding to the oxygen used in combustion is 
iV — 3.76 Ox. Hence, since the nitrogen undergoes no change, 
the percentage of excess air is 

X = 100 (3.76 Ox) -T- (iV - 376 Ox), . . (353) 
and the excess coefficient is 

376 Ox 



X 



1 + 



1 + 



(354) 



100 N — 376 Ox 

(j) In some cases it is possible to have incomplete combustion 
of part of the carbon although sufficient air is present, since the 
air may not be properly distributed. In such cases x and X 
can be determined if the volume per cent of CO is known in 
addition to the N and 0. Since each volume of CO present could 
have combined with half its volume of oxygen to form CO2, it 
follows that, on the basis of complete combustion, the excess 
oxygen is equal to — CO/ 2. The nitrogen accompanying this 
is 3.76 (0 — CO/ 2) , and that corresponding to the oxygen required 
for complete combustion is A/"— 3.76 (0 — | CO). The percentage 
of excess air for this case is, then 

^ 3.76 (0-1 CO) X 100 
"" N- 3.76 (0 - I CO) ' • • • ■ 
and the excess coefficient is 

376 (0 - i CO) 



(355) 



X 



100 



1 + 



(356) 



iV-376(0-iOO)- • 
(k) In case there is a deficiency of air amounting to y per cent, 
there is 2y per cent of the carbon burned to CO, as has already 
been shown (in Sect. 236 g) ; in burning one pound of carbon 
there will result 23;/ 100 X 2| pounds of CO, (l — 23// 100) X 3| 
pounds of CO2, and the nitrogen present will be (l — y/ioo) X 
(0.77 X 1 1.6) pounds. Tabulating these values gives: 

TABLE XXII. — FLUE GAS CONSTANTS. 



Gas. 


w 


V62 


w\ 


CO, 
CO 

N 


(l-2y/ioo)X3l 

(2y/ioo)X2i 

(l-y/ioo)X8.9 


8.62 
13.60 
13.60 


31.6 (l-23'/ioo) 

31.7 (2>i/l00) 

121 .0 {l—y/ioo) 



482 HEAT-POWER ENGINEERING 

The summation of the last column gives 

S (wV)n = 152.6 — 1. 21 y. 
Then, from Eq. (349), 

Per cent CO. by vol. = 31-6 (1 - 2 y/ioo) 

^ 152.6 - I.2I 3^ ^^^'^ 

and Per cent CO by vol. = 31-7 (^y/ioo) ^^^ _ . . 

^ 152.6 — 1.213; ^^"' ^ 

The relation of the percentage volumes of CO2 and CO in the 
flue gas to the percentage deficiency of air, is shown in Fig. 316 
by the curves to the left of oO. 

239. Temperature of Combustion, (a) When combustion 
occurs, the heat energy liberated tends to be dissipated. But if 
the combustion can be imagined to occur within a vessel perfectly 
impervious to heat, then all the liberated heat must remain 
within the vessel, and the products of combustion would be raised 
to a high temperature. This temperature is known as the theo- 
retical temperature of combustion and is readily calculated. 

(b) First, assuming only one gas as the product of combustion, 
and no heat absorbed by the surrounding vessel, the theoretical 
temperature rise will be obtained by dividing the available heat 
by the product of the weight and the specific heat of the gas 
formed. If the vessel is assumed not to change in size, the specific 
heat for constant volume must be used ; but if the vessel is the 
equivalent of one fitted with a movable piston so arranged as 
to maintain constant pressure, the specific heat would be that 
for constant pressure. 

For example take the reaction 

2 C + O2 = 2 C0]+ (4500 B.t.u. per pound of C). 

Since 2^ pounds of CO are formed per pound of carbon, the 
theoretical rise of temperature with the theoretical supply of 
pure oxygen will be 

R^se- ^^"^ 



C„X2|' 

in which C„ is either the specific heat at constant volume (C„), 
or at constant pressure (Cp), as the case may be. 

(c) If air is used to furnish the oxygen, the nitrogen must also 
be heated. Then, since the weight of N, accompanying the O 



COMBUSTION 483 

used per pound of C, is l\ X 77/23 = 4.47, the resulting temper- 
ature rise is 

Rise = 4500 



C„ X 2i + Cn' X 447 



in which the primed specific heat is for the nitrogen, and the other 
for CO as before. Similar equations may be written for other 
combustibles and other products of combustion. 

(d) The temperature theoretically attained will be the sum of 
temperature to existing before the start of the reaction and the 
temperature rise as found above. 

In general, for any number of products of combustion, 



i = to + 



Coivo +> CiWi + C2W2 + C3W3 + etc. 



'° + 2TtS); - • ■ • (359) 



in which 



^0 = initial temperature, 
AQ = heat liberated, 
Co, Ci, C2 = the specific heats of the products of combustion, 
at constant volume or pressure, as the case may 
be, and 
Wo, Wi, W2 = the weights of the products of combustion. 
The specific heats of the products of combustion * are given in 
Table I on pages 40 and 41. 

(e) It is evident that the larger the denominator of the frac- 
tion in Eq. (359) the lower will be the theoretical temperature of 
combustion. If, then, an inert gas such as nitrogen is carried 
through the heating process, as when air is used instead of pure 
oxygen, the theoretical temperature will be lowered; and should 
more air be supplied than is needed for complete combustion, 
the temperature will be still further reduced. Diluents, though 
taking no essential chemical part in the reaction, thus play a very 
important part from the physical side; they always reduce the 
theoretical maximum temperature attainable by the combustion. 

The way the temperature rise theoretically varies with excess 
or deficiency of air, when carbon is burned at constant pressure, 
is shown in Fig. 317. 

(f) If any heat is lost during the period of combustion, as, 

* See also (g) of this section. 



484 



HEAT-POWER ENGINEERING 



^ 5000 

Pq' 4000 
0. 

1 3000 
9 2000 



























/ 


^ 




\ 












/ 


^ 








\ 


\ 






















N 


v^ 




























— 




























50 40 30 20 10 

y j^Deflciency 



100 150 200 250 300 
X ft Excess 



Fig. 317- 



for instance, by radiation, the numerator of Eq. (359) will be 
diminished by the amount lost and the theoretical temperature 

rise will, of course, be 
decreased. This indicates 
the advisability of caus- 
ing combustion to take 
place as rapidly as pos- 
sible, because, despite the 
fact that the same a- 
mount of heat is liberated 
during slow as during 
rapid combustion, the ac- 
tual time allowed for radiation in the latter case is less, and 
hence, other things being equal, the temperature attained will 
be greater. 

(g) In the chapters on the theory of the ideal gas it was stated 
that for ordinary work the specific heats of real gases might be 
x:onsidered constant. They are, however, really not constants, 
and some of them increase rapidly in value at high temperatures. 
From the previous consideration of the behavior of superheated 
steam this is just what would be expected. 

There is still considerable lack of agreement between the 
values of the high temperature specific heats of gases as deter- 
mined by different investigiators. The later work in this field 
does, however, give sufficiently concordant results to definitely 
settle the fact that such increase with the temperature does 
occur, and to warrant the engineer in assuming some of the values 
obtained as sufficiently accurate for practically all engineering 
calculations. 

The values for mean specific heats given in Fig. 318, taken 
from curves prepared by Prof. G. B. Upton and published in 
■"Experimental Engineering" by Carpenter and Diederichs, repre- 
sent the most probable values for the different gases named. 
It will be noted that no account is apparently taken of variation 
of the specific heat with pressure. Such variation is negligible 
for most gases with which the engineer ordinarily deals, — the 
principal exceptions being water vapor and ammonia. For water 
vapor the variation with pressure is rapid at low temperatures 
but becomes less so at higher temperatures, as was shown in 
Fig. 40. 



COMBUSTION 485 

(h) Since the specific heat increases with temperature, the 
value of the denominator of Eq. (359) must increase when 
the numerator becomes greater, other things being equal; thus 
the higher the temperature the less effective is a given quantity of 
heat in causing a rise of one degree. It follows that in practical 
work, even if all radiation could be prevented, the temperature 
will never rise as high as Eq. (359) would indicate when the 
ordinary values of the specific heat are used. 



Mean_SpecificJE[eat 
(C„) at Constant 
^Pressure 



-472r0:30- 
i.l-LO.29 
t.O 



0:66 
0.64 

0:62 

-IOr27J-0^ 



To Obtain Mean Specific Heat(Cv) 
At Constant Volume Substract 
From Cp Tlie Following Constants :- 

O N Air CO2 HgO CO H 
0.063 0.072 0.069 0.045 0.112 0.009 l.QQ 




1000 1200 1100 1600 1800 2000 
Temp. Deg. Fahr. 



2100 2600 2800 3000 



Fig. 3i8. 



To determine the real temperature rise (neglecting radiation 
loss) for any given heat supply, the mean specific heats must be 
used in the denominator of the equation. The only satisfactory 
way of doing this would be to guess at the temperature expected,, 
choose the corresponding mean specific heats, determine the re- 
sultant temperature and compare with the value assumed. If 
the difference is great a closer approximation can be made, and 
so on. This is similar to many of the calculations used in con- 
nection with superheated steam. 



486 HEAT-POWER ENGINEERING 

240. Combustion of Hydrogen, (a) Hydrogen burns accord- 
ing to the following equation: 

2 iJ2 + O2 = 2 HiO (360) 

The weights combined are 

(2 X 2) of H+{2 X 16) 0/0=36 of H2O, 
and dividing this by 4 gives 

I of H + 8 of = 9of H,0 (361) 

Then, for each pound of hydrogen burned, 8 pounds of oxygen 
must be supplied, and 9 pounds of water will result. It is also 
found that about 62,000 B.t.u. are liberated per pound of hydro- 
gen burned. 

(b) Problems involving the combustion of hydrogen are often 
complicated by the fact that many of the real combustibles 
contain some oxygen, which may exist as a constituent of a 
CxHyOz compound, or in combination with some of the hydrogen 
as H2O, or in a number of other different ways. Obviously, to 
calculate the heat that would be liberated by a pound of such 
material would require a knowledge of the condition of all 
oxygen present; but unfortunately such knowledge is seldom 
available, hence it is customary to consider that all oxygen present 
is combined with hydrogen as H2O and that only the remainder 
of the hydrogen can burn to liberate heat. This combustible 
part of the total hydrogen is known as available or uncomhined 
hydrogen. 

According to the assumption just given, the " available " 
hydrogen can be determined in any case by subtracting from 
the total hydrogen the amount which could be combined with all 
the oxygen present. Equation (361) above shows that a given 
weight of oxygen could be combined with one-eighth its weight 
of hydrogen and it follows from this that the weight of the 
unavailable hydrogen must be one-eighth of the weight of oxygen 
present in a compound. 

Then if H represents the total weight of hydrogen present and 
if there are pounds of oxygen which are assumed to be already 
combined with part of this hydrogen, the available hydrogen 
must weigh ( H — 0/8) pounds. The oxygen required for the 
combustion of the available hydrogen is 

Pounds of = 8 (il - 0/8), .... (362) 



COMBUSTION 487 

and the weight of air required to supply this oxygen is found by 
multiplying this equation by 4.35; thus 

■ Pounds of air = 34.8 {H — 0/8) (approx.). . (363) 

(c) If hydrogen at 60° F. is burned to H^O and the latter is 
afterwards cooled to 60°, the quantity of heat obtained varies 
according to the conditions of cooling. If the material is con- 
tained in a vessel equivalent to a cylinder closed with a movable 
piston exerting a constant pressure and if at the end of the cool- 
ing process all the water exists as liquid, a certain amount of 
heat equal to about 62,000 B.t.u. (experimental value 61,950) per 
pound of available hydrogen will be obtained. In this book this 
will be called the " higher heat value " of hydrogen. 

On this basis the higher heat value may be defined as the 
quantity of heat obtained when the products of combustion are 
cooled in such manner that the water vapor resulting from the 
combustion of one pound of hydrogen (initially at 60° F.) is com- 
pletely condensed at constant pressure to a liquid at a tempera- 
ture of 60° F. Then, when a combustible containing H pounds 
of hydrogen and pounds of oxygen is burned, the heat obtained 
from the available hydrogen, on the basis of this higher heat 
value, would be 

B.t.u. = 62,000 {H - 0/8). 

(d) Other definitions of higher heat value are sometimes given. 
Instead of cooling to 60°, some other (higher) temperature, such 
as 212°, may be used, in which case the amount of heat involved 
is slightly less. 

Should the cooling be conducted in a vessel inclosing a greater 
volume than that occupied by the liquid water, only a part of 
the vapor will condense, the rest remaining to fill the surplus 
space at the existing temperature. This vapor will of course 
have associated with it its latent heat of vaporization, and there- 
fore the heat value found will be less than that obtained when 
all the water is condensed. 

(e) Another calorific quantity, known as the "lower heat 
value," is used by engineers but is not very accurately defined. 
It is generally assumed to be the heat obtained if all the water 
formed remains saturated or superheated vapor at the tempera- 
ture of the products of combustion. This would be numerically 



488 HEAT-POWER ENGINEERING 

less than the higher heat value already given, by an amount 
equal to the heat above 60° per pound of vapor in the flue gas. 

The accurate determination of the heat which could be ob- 
tained by cooling and condensing, under constant pressure, the 
water vapor contained in flue gases is more or less complicated 
in most cases. It is first necessary to determine the weight of 
vapor per cubic foot of gas, its partial pressure, and its tempera- 
ture. From this data its state can be determined either from 
steam tables, or from a diagram similar to that of Fig. 34 drawn 
for water vapor. With the state known, the heat which would 
be liberated per pound during cooling and condensing under 
constant pressure can be found from the steam tables. The 
same result can be closely approximated by the use of the follow- 
ing formula,* which gives very closely the heat above 32° F. per 
pound of water vapor in the air, or in products of combustion, 

A(2 = 1058.7 +0.455/1 B.t.u., .... (364) 
in which ! 

AQ = B.t.u. per pound above 32° F.; and 
ti = temperature of vapor in products of com- 
bustion (= temperature of gas). 

If it is assumed that the liquid resulting from condensation 
could be cooled only to the temperature ^2° F. (say the room 
temperature of about 60°, instead of to 32°), then, 

^Qh = (1058.7 + 0.455 ^1) - (^2 - 32) 

= 1090.7 + 0.455 /i - /2. .... (365) 

Thus, every pound of water vapor which escapes uncondensed in 
the products of combustion will carry with it an amount of heat 
equal to AQt^, which is, therefore, unavailable for other pur- 
poses. Since every pound of hydrogen burns to nine pounds 
of water, it follows that the lower heat value per pound of 
available hydrogen is 

L.H.V. = 62,000 - 9 (1090.7 -\- 0.455 h - ti). . (366) 

This expression shows that the lower heat value is really a 
variable, depending for its value on the lowest temperature ti 
attained by the products of combustion before leaving the 
apparatus which they are supposed to heat, and also on the tem- 

* For explanation of this formula and further details see " Experimental En- 
gineering," Carpenter and Diederichs, p. 467. 



COMBUSTION 489 

perature h, which is generally assumed as about 60°. For a 
value of h equal to 1500° F., and h equal to 60°, the difference 
between the lower and higher heat values is about 15,000 B.t.u.; 
for ^1 equal to 500° F. the difference equals about 11,000 B.t.u.; 
and for h and tz both equal to 60° F. the difference is still about 
9500. 

(f) The value ordinarily used for engineering purposes, and 
which may therefore be called the " engineering lower heat 
value," is generally taken at 52,000, which corresponds to a 
value of h equal to about 530° F. with h = 60° F. It is evident 
that this may be merely a very rough approximation in many 
cases. 

When this value is used, the lower heat value of the hydrogen 
in a fuel which contains H pounds of that element and pounds 
of oxygen is 

B.t.u. ^ 52,000 {H -0/8) (367) 

(g) In some cases it is more convenient to use heat values per 
cubic foot of hydrogen rather than per pound. These can easily 
be obtained by dividing the values already given by the specific 
volume of hydrogen. There will obviously be as many different 
values as there are temperature and pressure combinations; 
hence the conditions under which the cubic foot of gas is to be 
measured should always be specified. At a temperature of 
32° F. and under a pressure of 14.7 pounds per square inch the 
specific volume of hydrogen is 178 cubic feet. Therefore, the 
heat values per cubic foot under these conditions are 

Higher heat value = — '—--- = 348 B.t.u. . . (368) 
17s 



and 



Lower heat value = ' = 292 B.t.u. , . (369) 
178 



(h) In this connection it should be noted that although the 
heat value per pound of hydrogen is considerably higher than 
the heat value per pound of carbon monoxide, the values per 
cubic foot of material are more nearly equal. Thus the value 
per cubic foot of CO at 32° F. and at atmospheric pressure 
is about 335 B.t.u., which is but slightly less than the upper 
value for hydrogen and is considerably greater than the lower 
value. 



490 HEAT-POWER ENGINEERING 

This relation is of particular importance in engineering, 
because : 

(i) There are a large number of commercial gases containing 
both hydrogen and carbon monoxide and it is possible to regu- 
late the relative proportions of the two to a certain extent. 

(2) It is generally the volume of the gas which is to be handled, 
and not its weight, which determines the dimensions and cost 
of apparatus and cost of operation ; and 

(3) Under most engineering conditions it is the lower heat 
value of hydrogen, not the higher, that is made available. 

241. Hydrocarbons, (a) Combustibles composed of hydro- 
gen and carbon in combination are known as " hydrocarbons." 
There are many kinds which differ as to the relative proportions 
of H and C contained. They burn to form the ultimate products 
CO 2 and H-iO, but the process is often very complicated. The 
exact combustion behavior of all the common hydrocarbons is 
not yet well known but experiment shows that in many cases a 
number of reactions go on before the actual combustion process 
is completed. 

(b) It is very common practice to assume that when a hydro- 
carbon containing C pounds of carbon and H pounds of hydrogen 
is burned it should liberate 

(C X 14,600) + (iJ X 62,000) B.t.u., . . (370) 

but such calculations seldom check with the actual values. This 
is explained in part by the fact that the hydrocarbon is already 
a chemical compound and must be broken up to enable the indi- 
vidual elements to combine with oxygen. When this occurs 
a quantity of heat must be absorbed or liberated, thus diminish- 
ing or increasing the amount liberated during the formation of 
CO2 and H2O. Many empirical formulas have been developed 
to take account of such effects, but none of them are entirely 
satisfactory for all cases. 

(c) In many instances the approximate calculation by Eq. 
(370) is sufficiently exact, but when great accuracy is desired a 
determination should be made by using a " Fuel Calorimeter," 
which will be briefly described in Section 244. 

The experimentally determined and calculated calorific values 
of several of the principal hydrocarbons are given in Table XXIII. 



COMBUSTION 



491 



TABLE XXIII. — CALORIFIC VALUES OF HYDROCARBONS. 



Name. 


Molecular 
Formula. 


Weight in 

Lbs./Cu. Ft., 

Atm. Pres. and 

32° F. 


Calorific Value Experimentally 
Determined, B.t.u./Lb. 


Calorific Value 
Calculated,, 
B.t.u./Lb. 




Higher. 


Lower. 


Higher. 


Methane 

Ethane 

Ethylene . . . 
Acetylene.. . 


CH, 
C2H, 

C,H2 


. 04464 
0.08329 
0.07809 
0.07251 


23,842 
22,399 
21,429 
21,429 


21,385 
20,434 
20,025 
20,673 


26,455 
24,080. 

21,370 
18,240 



242. Combustion of Sulphur. Sulphur burned in oxygen 
forms sulphur dioxide. The reaction is given by the equation 

S + 02 = 302. .*..... (37i> 
The weights combined are 

32ofS+(2X 16) of = 640/ SO2, 
and dividing by 32 gives 

iofS-\-iofO = 2of SO2 (372) 

Then, for each pound of sulphur, one pound of oxygen is needed 
for complete combustion and 2 pounds of SO2 result. To furnish 
the pound of oxygen approximately 4.35 pounds of air are 
required. The reaction is accompanied by the liberation of 
about 4000 B.t.u. per pound of sulphur. 

243. Combustion of a Mixture of Elements, (a) If the sym- 
bols represent the pounds of each of the respective elements 
present in a mixture, and if it is supposed that the oxygen present 
is already in combination with hydrogen, then, from the pre- 
ceding paragraphs, it is evident that for complete combustion 
there are needed 

Pounds of Oxygen = 2^ C -\- 8 (H - 0/8) + S; (373) 

to furnish this would require 4.35 times as much air, or 

Pounds of Air = 1 1.6 C + 34.8 (H - 0/8) + 4.35 S; (374) 

and the volume of this air at a temperature of 62° F. and at 
atmospheric pressure is found by multiplying by the specific 
volume 13.14 (from Table XX), giving 

Cubic Feet of Air = 153 C + 454 (H - 0/8) + 57 S. (375) 



492 HEAT-POWER ENGINEERING 

The volumes at other temperatures and pressures can be found 
from the relation {PV/T)i = (PV/T)^. 

(b) The heat liberated when such mixtures are burned can be 
conveniently determined by the use of what are known as 
Dulong's formulas. These are: 

Higher B.t.u. = 14,600 C + 62,000 {H - 0/8) + 4000 5. (376) 
Lower B.t.u. = 14,600 C + 52,000 (H — 0/8) + 4000 5. (377) 

It will be noted that these formulas are merely the summations 
of the heat values given before for the individual elements. 

As already explained, if there are chemical combinations 
which must be broken up, the heat associated with the separa- 
tion must be considered besides that given by Dulong's formula. 
Thus Eqs. (376) and (377) do not apply to hydrocarbons, al- 
though their use. wilf give the approximate heat values. 

244. Fuel Calorimeters and Heat Value, (a) In the absence 
of satisfactory methods of calculating the heat liberated during 
combustion, the scientist and the engineer have developed in- 
struments, known as Fuel Calorimeters, for measuring the energy 
as liberated. 

Practically all of them operate in the following way : A known 
weight, or volume, of the combustible is burned within the in- 
strument under such conditions as to insure as nearly as pos- 
sible complete combustion, and the heat liberated is absorbed by 
water or similar liquid in an enveloping jacket. By measuring 
the temperature rise of the liquid, and correcting for radiation 
loss from the instrument, the heat liberated is obtained; and from 
the known weight of the material burned, the heat which would 
be liberated per unit weight may be calculated. This value is 
known as the Heat Value, Calorific Value, or Heat of Com- 
bustion of the material. In engineering work it is generally 
expressed in B.t.u. per pound of material, or, in the case of gases,* 
per cubic foot at standard conditions. 

(b) In all calorimeters the jacket temperature is near that of 
the room and the products of combustion are cooled to approxi- 

* It is almost standard practice to use weight as the basis for solid fuels and • 
volume as the basis for gases. For liquids both weight and volume are used, 
though weight is probably given the preference. Whenever there is a possibility 
of confusion the unit should be given in the statement of results. If a cubic foot 
of gas " at standard " is used, the so-called standard should be defined. 



COMBUSTION 493 

mately the temperature of the jacket before leaving the instru- 
ment; thus the heat measured is generally assumed to be that 
obtained by bringing the products of combustion down to the 
initial temperature of the combustible material. This is seldom 
really accomplished and an error from this source is therefore 
introduced into practically all commercial calorific determina- 
tions. This method gives what is commercially called the 
" higher heat value," when the combustible contains available 
hydrogen. 

It has already been pointed out that even with the tempera- 
ture of the combustion products reduced to 60° F. there may be 
a considerable discrepancy between the values thus obtained 
and the true higher value. 

An accurate method of stating calorific values would be ta 
give the heat liberated when material at 32° F., or 60° F., is 
burned and the products are cooled to the original temperature, 
allowance being made in each case for humidity in the products, 
of combustion. In the present state of the art, however, such 
refinements are not warranted. 

245. Flue Gas Analysis, (a) In connection with tests of 
furnaces, boilers, and similar apparatus in which fuel is burned, 
it is often necessary to analyze the flue gases in order that certain 
efficiencies and losses can be calculated and that the conditions 
of combustion can be determined. In these analyses the quanti- 
ties of gases present are generally expressed in " volume per- 
centages." For example, gases a, b, and c may be said to con- 
stitute respectively 10 per cent, 20 per cent, and 70 per cent of 
the total volume ( = 100 per cent) resulting from their mixture. 

(b) In making the analysis, a measured volume of the mixed 
gases at atmospheric temperature and pressure is successively 
brought into contact with appropriate reagents, each one of 
which absorbs but one constituent gas; then, by noting the 
corresponding decreases in volume under atmospheric conditions, 
the volume-percentages of the various constituent gases can 
readily be determined. 

(c) To give a clearer idea of this process, assume that the 
cubical vessel shown in Fig. 319 (a) incloses a volume of 1 00 units, 
that it is filled with a mixture of gases, say CO2, CO and N, 
and that the pressure of the mixture is atmospheric. Each of 



494 



HEAT-POWER ENGINEERING 



/Constituent /' 



Fig. 319. 



the constituents evidently occupies the entire volume, that is, 
each is evenly distributed throughout the vessel ; each exerts a 
definite " partial pressure "; and the sum of these partial pres- 
sures equals the atmospheric pressure. If it were possible to 
collect each of the constituents and isolate it from the others by 
flexible diaphragms, as shown in Fig. 319 (6), and if each of the 
constituents were decreased in volume 
until its pressure became equal to 
atmospheric, then the sum of all the 
volumes would equal the original vol- 
ume, provided the temperature re- 
mained the same. That this is true 
will be shown in the following para- 
graphs. 

''{d) Assume, for instance, that in Fig. 319 (a) the partial pres- 
sures are aPa, bPa, and cPa, a, b, and c being fractions and Pa 
being atmospheric pressure. If the total pressure of the mixture 
is atmosjDheric, the sum of the three partial pressures must 
equal Pa, that is 

aPa -\- hPa +cPa = Pa, or a + b+c = l. 

If the volume of the vessel is V, then the constituent with 
pa'rtial pressure aPa will have to be given a volume 

Fi = (F X aPa) ^ Pa = aV, 

in order to raise it to atmospheric pressure when isolated ; the 
constituent with partial pressure bPa will have to be given a 
volume ¥2= bV; and the remaining constituent, a volume 
F3 = cV. 

From the relations between a, b, and c it is obvious that 

Fi + F2 + F3 = F ( = 100 by assumption). 

(e) Thus a, b, and c not only represent the partial pressure 
fractions, but also give the fractions of the total volume that 
would be occupied by the constituents when reduced to the 
volumes they would have when isolated and raised to atmos- 
pheric pressure without change of temperature. As was stated, 
the so-called percentage by volume of any constituent is there- 
fore merely the percentage of the original volume of the mixture 
which that constituent would occupy if existing alone at the 



COMBUSTION 495 

same pressure as that exerted by the mixture and at the same 
temperature. 

(f) It is important to note in connection with flue gas analyses 
that the water vapor content is never determined in ordinary 
engineering apparatus. The greater part of this water is con- 
densed and disappears by mixing with water contained in the 
apparatus used in making the analysis. The gaseous mixture 
is, however, practically always saturated with water vapor during 
the entire analysis, and although this water exerts a partial 
pressure, this latter affects each of the constituents proportion- 
ately, • hence its influence is really negligible. Though water 
vapor is present the results on the percentage basis are therefore 
the same as those for dry gas. 

246. Weight of Flue Gases, (a) In many engineering com- 
putations it is necessary to determine the weights of the gases 
resulting from the combustion of a given fuel under given con- 
ditions. Such calculations are simple when one knows (i) the 
analysis of the flue gases, (2) the analysis of the fuel, and (3) the 
moisture content of the air. 

(b) As was seen in the preceding section, the volumetric 
analysis of the flue gas is the equivalent of isolating the con- 
stituent gases and reducing them to the same pressure and 
temperature. Then from Avogadro's hypothesis it follows that 
the number of molecules of each of the gases present must be 
directly proportional to the volumes (F) which the gases occupy, 
hence the products {mV) of these volumes by the respective 
molecular weights (w) of the gases, give measures of the rela- 
tive proportions by weight of the gases present in the mixture; 
the sum (2m V) of these products gives a measure of the weight 
of the whole mixture; and the weight percentage of any con- 
stituent is evidently 

Per cent weight = mV -^ 2wF. . . . (378) 

Thus, if the mixture is composed of CO2, 0, CO, N, H, and SO2, 
and if the relative volumetric proportions of the constituents 
are represented by their chemical symbols, then the equivalent 
molecular weight of a unit volume of the mixture is 

2wF = {44 CO2 -\-32 0-\-28C0+28N-\-2H-{-64 SO2), (379) 



496 HEAT-POWER ENGINEERING 

and the weight percentage of CO2 for example is found by divid- 
ing 44 CO2 by Eq. (379). 

(c) It is generally most convenient to express the constituents 
in terms of their weight per pound of carbon burned. The weight 
corresponding to the m V value of the carbon represented in Eq. 
(379) is evidently 

Weight of C = 12(002 + CO); • • • (380) 
hence the weight of any constituent per pound of carbon is found 
by dividing its mV value by 12 (CO 2 + CO). Thus, the weight 
of nitrogen is 

WN = 28N ^ 12 (CO2 + CO) ; per lb. of C . . (381) 
the weight of free hydrogen is 

WH = 2H^ 12(002 + 00); . . . (381a) 
and similarly for the other constituents. 

The total weight (w) of dry gas mixture per pound of carbon 
actually burned is given by dividing Eq. (379) by Eq. (380). 
When simplified this becomes 

11CO2 + 8O + 7 (CO + N) + H/2 +16SO2* , o ^ 

^ = 3(C02 + C O) ' (382) 

in which, as before, the symbols represent the relative volumes 
of the gases they symbolize. 

(d) To find the total weight of "wet" gases per pound of car- 
bon, it is necessary to add three more items: 

(i) The weight of water, in the fuel per pound of carbon, as 
found by analysis; 

(2) The weight of water carried by the air supplied for com- 
bustion, per pound of carbon, which can be found from psy- 
chrometric observations ; and 

(3) The weight of water formed by the hydrogen burned, per 
pound of carbon. This can be found as follows, when the fuel 
analysis is known: Let wh be the weight of free hydrogen, per 
pound of carbon in the fuel, and letH, as before, be the volume of 
hydrogen not burned (per pound of C), as found in the analysis 
of the flue gases; then wh ~ {2 H -^ 12 (CO2 + CO)} is the 
weight of hydrogen burned, and the resulting weight of water is 

Weight of H2O = 9 {WH-[2H -^12(002 + CO)] \ (383) 

* If the gases CHi and CnHm are present, this expression should have 
4 CHi -\- 7 CnHm added to the numerator, and the parenthesis in the denominator 
should include CH4 + 2 CnHm, it being assumed that the CnHm is all Ethylene 



COMBUSTION 497 

247. Percentage of Excess Air. It is now possible to derive 
perfectly general expressions for the percentage of excess air 
and for the excess coefficient, — that is, expressions which are not 
limited, as are Eqs. (352) to (355), to the case of the combustion 
of carbon alone. 

If the symbols represent relative volumes as before, then, accord- 
ing to Eq. (381) the total weight of nitrogen in the flue gases per 
pound of carbon is 28 iV -^ 12(002 + CO), or 7 N -^ 3(C02+ CO) ; 
hence, the oxygen which accompanied this nitrogen must be 

Total oxygen = ^ X 3 (^ J^ + CO) P^^^^"' ' ^^^4) 
The weight of oxygen not used is, similarly, 

32 ^ 12 (CO2 + CO) = 8 ^ 3 (CO2 + CO), 
where is its volume, which is assumed to be known from the 
volumetric analysis of the flue gas. But part of this unused 
oxygen could have been utilized had combustion been perfect. 

_ . . .16^ 28 CO 4 CO 

ihus a weight equal to — X ~ 



28 '^ 12 (CO2 + CO) 3 (CO2 + CO) 
might have been used for burning the CO to CO2; and a weight 

"^^^^ ^° ^ X 12 (CO2 + CO) = 3(C0^2 + CO) "^'^^^ ^^^" ^^"^ 
used for burning the free hydrogen in the flue gas. The true 
weight of excess oxygen per pound C is, therefore. 

Excess = [8 0-4(C0+iJ)] ^ [3 (CO2 + CO)] (385) 
Subtracting this from the total oxygen (Eq. (384)) gives the 
weight of required oxygen, per pound of C as 

^X7N-[80-4iCO+H)]* 

Required oxygen = ^ (^CO. -{- CO) ' ^^^^"^ 

Then, since the percentage of excess air, x, is equal to excess air 
(or oxygen) divided by the total air (or oxygen), it follows that 
I 8 0-4(CO+i7) I 

^^|f^X7iV-[80-4(CO+i?)]p^°^-^ • ^^'^^ 

* If the gases CHi and CnHm are present, 4 CHi + 7 CnHm should be added 
to the parenthesis in the numerator and CHi + 2 CnHm should be included in that 
in the denominator. 

t To account for the gases mentioned in the two preceding footnotes, 
4 CH4, + 7 CnHm should be added in the parentheses in the numerator and 
denominator. 



498 HEAT-POWER ENGINEERING 

The excess coefficient, X, is therefore 

X = . +4 = . ^ (^ j . (333, 

[^X7Ar-!80-4(CO + if)]| 

248. Stack Losses, (a) In connection with tests of furnaces, 
boilers and similar apparatus it is customary to determine the 
amount of heat carried away by the gases passing up the stack, 
or as it is often called the " heat lost in flue gases." 

(b) Before taking up the complete method of calculating these 
losses, a simplified theoretical discussion will be considered in 
order to bring out certain fundamental relations. For this 
purpose the case of dry carbon only, burned with dry air, will 
be analyzed. In connection therewith the combustion may 
occur under any one of three sets of conditions, as follows: 

Case I. Complete combustion with theoretical air supply; 
Case 2. Complete combustion with excess air; and 
Case 3. Incomplete combustion with deficiency of air. 
It is obvious that Case i is merely a limiting value between 
Cases 2 and 3, and hence need not be considered separately. 

(c) With Excess Air (Case 2) the only loss to the stack under 
the assumed conditions is that due to sensible heat of the CO2, 
the nitrogen, and the excess air in the flue gases. 

It was shown in Sect. 238 (f), that with x per cent excess air 
the so-called "products of combustion" resulting from the 
complete burning of one pound of carbon would consist of 3.67 
pounds of CO2, 8.9 pounds of N and o.ii6x pounds of air; 
hence the total weight of flue gas, per pound of carbon, is given 
by the equation. 

Pounds of flue gas = 3.67 + 8.9 + o. 1 16 x . . (389) 

As this waste gas leaves at a temperature considerably higher 
than that at which the constituents entered the furnace, it 
carries with it sensible heat which should have been used. 
With weight determined the corresponding loss of heat can 
readily be computed when the specific heat and the temperature 
of the flue gas are known. 

As flue gases of boiler furnaces generally leave with a tempera- 
ture less than 700° F., it is customary to neglect the variations 
of the specific heats with temperature, and as the specific heat 
of the flue gas is nearly the same as that of air, it is also customary 
* See last footnote on page 497. 



COMBUSTION 499 

to neglect the change with variations in x. The specific heats 
assumed for the mixture by different writers generally fall 
between 0.22 and 0.24; with average excess coefficients, 0.24 
is a satisfactory figure. With this assumption, the approximate 
formula for loss of heat in the flue gas, per pound of carbon 
burned, for Case 2 is 

B.t.u. loss = 0.24 {3.67 + 8.g + o.iidx) {tf — to), (390) 

where tf is the temperature of the flue gas and ta is the atmos- 
pheric temperature. Since each pound of carbon should liberate 
14,600 B.t.u. the per cent loss of heat is given by 

_, - o.24(j.67-h8.Q-^o.ii6x)X(tf — ta)^^ f X 

Per cent loss ^ — ^^ — - — -2 — ^ X 100. (391) 

14,600 ^^ 

Values obtained from this equation are plotted in the upper, 
right-hand quadrant of Fig. 320 and the resulting curves serve 
to show how the stack loss varies with different values of x and 
of (// — ta). Actually, because of increases in the specific heats 
with temperature and excess air, the losses would increase some- 
what more rapidly than these curves show. 

(d) With Deficiency of Air (Case 3 above) there are two stack 
losses to be considered — that due to sensible heat, and that due 
to the heat value of the CO (or of the CO and C) not burned. 

The weights of gas (per pound C) present with y per cent 
deficiency of air will be given by (from (k) of Sect. 238) 

Pounds of Flue Gas = 3.67(1 - ^]of CO2 + 2.33^ of CO 
•^ \ 100} •' ^^ 100 •" 

+ 



eat 0.24, this would give, per pc 
to sensible heat of 

iB,.u.)s^o.4[3.67{r-^y^.33^„+8.9{t-^^^ 



Assuming the specific heat 0.24, this would give, per pound of 
carbon, a stack loss due to sensible heat of 



\{tf-ta). 
(393) 

Since each pound of CO could give 4300 B.t.u. if burned, there 



is also, per pound of C, a loss due to the CO equal to 

{B.t.u.)co = 2.33 X -^ X 4300 . . . 
provided the deficiency (y) is not greater than 50 per cent. 



500 



HEAT-POWER ENGINEERING 



The total loss with deficiency of air less than 50 per cent is 
evidently equal to (B.t.u.)s + {B.t.u.)co- This has been plotted 
in the lower right-hand quadrant of Fig. 320 for different tem- 
peratures of gas. 

If 3' exceeds 50 per cent some of the carbon is not burned at all 
and the losses would therefore be still greater. However, as this 
is a case not ordinarily approached in practice it need not be 
considered here. 



1 










-M -t 


// 


/ 










f 


s 


^I'&i 


r 










a 


L 


"'t^ 


U/ 












/ 






'/ 








^i' 




jW 


' 3 


' i 

3O2& c 


V'" 


'X 


•10 ^ 


^ 


' 6 

i Loss c 


' 8 
fHeat 


) 'lOO 




tSS- 


X 


fe. ■ 


-30 g. 














^ 




\ 


•50 1 






^ 














,0^ 
■70 ^'- 








\ 












■90 
100 








\ 



Fig. 320. 

The losses resulting from a deficiency of air are shown in the 
lower right-hand quadrant of Fig. 320. 

(e) The completed chart of Fig. 320 includes the curves pre- 
viously given in Fig. 316, and serves to show in a general way how 
the losses vary with different temperatures, different quantities 
of air and different flue gas analyses. It must be borne in mind 
that certain broad assumptions were made to simplify the deriva- 
tion of this chart and it is therefore only approximately correct. 
From an inspection of the curves it at once becomes apparent 
that losses due to excess air are much less than those due to 
deficiencies, for example, with flue gas at 500 degrees, the loss 
occasioned by 100 per cent excess air is equalled by that due to 
only about 8 per cent deficiency. 



COMBUSTION 501 

In using the chart, however, it is important to note that com- 
parisons of losses incident to using different percentages of excess 
air should not necessarily be made on the basis of the same 
temperature — for, ordinarily, larger amounts of air bring about 
a reduction in temperature of the flue gas. 

(f) The foregoing applies to the combustion of carbon alone. 
In the actual case the " flue gas " usually contains CO2, CO, N, 
O, H, hydrocarbons and water vapor and therefore differs some- 
what from the case just considered. The stack losses in the 
actual case may be conveniently divided into three distinct 
parts : 

(i) That part represented by the sensible heat of the dry flue 
gas, not including the moisture that may be present; 

(2) That part due to incomplete combustion of some of the 
constituents of the fuel — this includes the potential heat of the 
unburned C (in the smoke) , CO, H and hydrocarbons ; 

(3) That part represented by the latent and sensible heat of 
the water vapor {moisture) in the flue gas. 

The methods of determining each of these losses will now be 
considered. 

(g) The weight {w) of dry flue gas (per pound of carbon) in the 
fuel can be found by Eq. (382) in Sect. 246 and it is common 
practice to use 0.24 for the Cp of the mixture. Hence the approxi- 
mate loss in the sensible heat in the dry flue gas (per pound of 
carbon burned) is 

(B.t.u.)s = o.24w(tf- to) (395) 

(h) A more accurate method of finding this loss is to first 
determine (as in Sect. 246) the weight (w„), per pound_of C, of 
each of the constituent gases, get its mean specific heat Cp^ from 
Fig. 318 for the temperature range, then compute the sensible 
heat it carries away; and finally take the summation for all the 
constituents. Thus the total sensible heat carried away by the 
dry flue gases is (per pound of carbon burned) 

(B.t.u.)s = S {wCp)n X{tf-ta) . . . . (396) 
(i) The stack loss due to incomplete combustion is (per pound 
of C)* 

{B.t.u.)i= CXi4,6oo + COX430o+H{52,i83- 4.095 tf+9ta), 

(397) 

* Neglecting hydrocarbons. 



502 HEAT-POWER ENGINEERING 

in which the symbols represent weights (per pound of C) of 
the respective substances, and the parenthetical quantity is ob- 
tained by subtracting from 62,000 (which is the higher heat 
value of H) the value g {logo.y -\- 0.455 h ~ Q as previously^ 
given in Eq. (366) . 

(j) The heat loss due to the moisture in the flue gas depends 
on the source of this water vapor. That moisture which is 
humidity in the air used for combustion is already vapor and 
merely becomes superheated in the furnace; hence the heat it 
carries away is, per pound of C, 

{B.Lu.)^=AXCAtf-ta), (398) 

where A is the weight of moisture in the air used per pound of C. 
The loss of heat due to the moisture (M pounds per pound 
of C) originally in the coal and due to the water formed by the 
combustion of hydrogen (M' pounds per pound C) is, from Eq. 
(366), 

(B.Lu.M = {M-\r M') {1090.7 + 0.455 if -Q • • (399) 

per pound of C. 

The total loss of heat per pound of carbon in the fuel is 

therefore, (B.t.u.)s + {B.t.u.)i + {B.t.u.) ^ + {B.t.u.)M- 



CHAPTER XXIX. 

ACTUAL COMBUSTION OF FUELS — FURNACES AND STOKERS — 
OIL BURNERS. 

249. Introductory. In a preceding chapter the physics and 
chemistry of combustion were discussed for theoretical cases 
only. The study of the actual process of combustion in furnaces, 
which will now be taken up, is more complicated because of 
the wide variation in composition of the fuels and because there 
is a great diversity of conditions under which the combustion 
takes place. In fact, there are so many variables involved that 
it is substantially true that in no two distinct cases does com- 
bustion occur under identical conditions; and even in the same 
furnace the conditions are constantly varying. It is, therefore, 
impossible to give detailed discussion of all the possible cases 
which might occur. There are, however, certain broad general 
principles, which, if understood, will be of great value in the 
solution of problems of combustion which arise in actual furnace 
operation and these will be brought out in the discussion which 
follows. 

250. Air Supply, (a) In the actual case, as in the theoretical 
one, it is essential that there be furnished a proper amount of 
air to supply the oxygen needed for combustion. The exact 
quantity necessary depends on the composition of the fuel and 
can readily be computed by the method given in Sect. 243, if 
the chemical analysis is known. The approximate amount of 
air required is often determined, however, by assuming that the 
combustible part of the fuel is pure carbon, each pound of which 
requires 11.6 pounds of air for complete oxidation and results 
in 12.6 pounds of flue gas. But, for most practical purposes it 
is sufficiently accurate, and is on the side of liberality, to assume 
the entire weight of coal to be composed of carbon, and then use 
these same values as per pound of coal. It should be noted, 
however, that the richer the fuel is in combustible hydrogen the 

503 



504 HEAT-POWER ENGINEERING 

greater will be the proportion of air needed, since one pound of 
hydrogen requires 34.6 pounds of air or about three times as 
much as is needed per pound of C. 

(b) In the ideal case, with fuel containing only carbon, each 
per cent deficiency of air has been seen to result in i .4 per cent 
loss of heat because of incomplete combustion (Sect. 236 (g)). 
As the same thing is substantially true in the actual case, great 
care must be exercised to insure an adequate supply of air at all 
points in the fuel bed. As the bed usually varies in thickness 
and in compactness and texture, the air will meet with less 
resistance in passing through certain portions than through 
others. Hence to insure against a deficiency at any point, it is 
necessary to furnish an amount of air somewhat in excess of what 
would theoretically be required if it were uniformly distributed 
and properly mixed with the combustible material. Excess air 
is not without its disadvantages, however, as it dilutes the 
furnace gases and lowers their temperature, which results in a 
decrease in the boiler efificiency. Although its presence is thus 
detrimental, it is much less so under ordinary conditions than is 
a deficiency, as was made clear in Fig. 320. Hence excess air 
should always be present but in as small amount as is consistent 
with satisfactory combustion. Usually an excess coefficient 
X of from 1.5 to 2 times the theoretical amount, on a basis of 
carbon, is used, i.e., from 18 to 24 pounds of air per pound of 
combustible. And, as before, it is usually sufficiently accurate 
to assume the whole of the coal to be carbon, and to use these 
values as per pound of coal. Experience shows that if less than 
1.3 times the theoretical quantity is used, the amount of CO 
formed is generally prohibitive even if the greatest care is 
exercised in operating the furnace.* But even if the air supply 
is adequate it does not follow that the combustion is complete, 
as will be seen in the next section. 

(c) With pure carbon as the fuel and with the theoretical air 
supply, there would be about 21 per cent by volume of CO2 in the 
flue gas, as was shown in Sect. 238 (c). Excess air will result in 
a decrease of the volume per cent of CO2 in the manner shown by 

* Even when considerable excess air is furnished there may be some CO formed 
in the thicker and more compact portions of the fuel bed because of local deficiency 
of air. Further, flue gas analyses may also show CO which was formed by processes 
which will not be discussed until later. 



ACTUAL COMBUSTION OF FUELS 



505 





\ 














\ 














\ 
















\ 














\ 
















^? 














;\ 


\ 


ji 













~1~ 











i 


> 9 12 15 18 i. 



the curve in Fig. 321. As the combustible part of the coal is 
mostly carbon these same percentages hold substantially in the 
actual case.* Thus, a knowledge of the CO2 content in the flue 
gas indicates in a general way the operating conditions within 
the furnace and enables the boiler attendant to intelligently 
adjust the air supply. 

Experience has shown that if the supply of excess air is such as 
to give CO2 by volume between 10 per 
cent and 15 per cent, the furnace will 
be operating at its highest efficiency, 
the exact best percentage varying 
with different conditions. A value 
below 10 per cent nearly always in- 
dicates too great an amount of air '■^^i, 
and a value above 15 per cent is ^ 
generally indicative of too small an 
amount, as it is usually accompanied 
by the formation of prohibitive quan- 
tities of CO. In Fig. 321 the region 
for the best results is that shown by 

the portion of the curve lying between (a) and (b) ; in Fig. 320 
it falls between the points bearing similar letters; and it ap- 
proximately corresponds with excess coefficient (X) between 1.3 
and 2.0, given in (b) of this section. 

(d) In order that the boiler attendant may obtain an indica- 
tion of the amount of air being supplied, various devices known 
as CO2 Recorders, Econometers, Combustion Recorders, Com- 
posimeters, etc.f are used to indicate the CO2 content of the flue 
gases. Some of these appliances operate, or indicate, intermit- 
tently, some continuously, and some give a continuous graph- 
ical record so that the owner or manager of the plant can check 
the operation over any desired period of time. In the use of all 
these instruments it is, of course, necessary to obtain samples of 
gas truly representative of the average and to guard against the 
infiltration of air through the boiler setting or the flues between 
the furnace and the sampling point. 



f, COo in Flue Gas by Volume 



Fig. 321. 



* Although the percentage of CO2 is somewhat less because of the other combus- 
tible and noncombustible constituents present in the flue gas in the actual case. 

t For description and method of using such apparatus see Carpenter and Diede- 
richs, " Experimental Engineering," published by John Wiley & Sons. 



5o6 HEAT-POWER ENGINEERING 

251. Conditions for Complete and Smokeless Combustion. 

(a) If air is passed upward through a deep bed of ignited carbon 
devoid of volatile matter, there is a tendency for any CO2 that 
is formed in lower layers to be reduced to CO when coming into 
contact with the carbon above. If this CO is not subsequently 
supplied with a proper amount of air while still at a high tempera- 
ture it will pass oflf unoxidized and this will result in a loss of heat 
which would otherwise be made available. It is, therefore, 
important that an adequate air supply and a suitable tempera- 
ture be maintained in the upper part of, and just above, the bed 
of fuel. This air may either pass through the bed or be supplied 
from above. 

The foregoing applies of course to the combustion of coke 
and charcoal as well as to carbon. Anthracite coal, which is 
mostly fixed carbon, behaves similarly, but in this case there is 
also a small amount of volatile matter which must be properly 
burned. These fuels, which have little or no volatile matter, 
give short flames above the fuel bed, the flames being due to the 
combustion of CO and the small quantity of volatile matter 
present. 

(b) When coal possessing a considerable amount of volatile 
matter is placed on a hot bed of fuel, the greater part of the vola- 
tile portion distills off as the temperature rises, and the residue, 
which is coke, burns in the manner just described. The more 
serious problem that confronts the engineer in this case is the 
complete oxidation of the combustible part of this volatile mat- 
ter. Evidently in the ordinary up-draft furnaces that are fired 
from above the combustion of this part of the fuel must occur 
above the fuel bed, just as is the case with CO; and in order that 
the combustible gases may be completely burned, the following 
four conditions must exist: 

(i) There must be sufficient air just above the fuel bed, supplied 
either from above or through the fuel bed itself; (2) this air 
must be properly distributed and intimately mixed with the com- 
bustible gases; (3) the mixture must have a temperature suffi- 
ciently high to cause ignition (some of the combustible gases, 
when mixed with the burned gases present above the fuel, have 
an ignition temperature of approximately 1450° F.) ; and (4) 
there must be sufficient time for the completion of combustion, 
that is, the combustion must be complete before the gases 



ACTUAL COMBUSTION OF FUELS 507 

become cooled by contact with the relatively cold walls of the 
boiler (which are at a temperature of about 350 degrees) or with 
other cooling surface. 

(c) To prevent the stratification of the air and gases, special 
means are sometimes adopted, such as employing steam jets 
above the fire and using baffle walls, arches, and piers in the 
passage of the flame, to bring about an intimate mixture. 

(d) In order that the air used above the fuel bed shall not 
chill and extinguish the flame, it should be heated either by 
passing it through the fuel bed, or through passages in the hotter 
parts of the furnace setting, or in some other way before mingling 
with the gases; or else the mixture of gases and air should be 
made to pass over or through hot portions of the fuel bed, or 
should be brought into contact with furnace walls, or other brick- 
work, which is at a temperature sufficiently high to support the 
combustion. 

(e) In order that the flame shall not be chilled and extinguished 
by coming in contact with cold objects, it should be protected 
by the hot furnace walls until combustion is complete. The 
furnace should have proper volume to accommodate the burning 
gases, and, when the conditions are such that the flame is long, 
the distance from the fuel bed to the relatively cold boiler sur- 
faces with which the gases first come in contact, should be at 
least as great as the length that the flame attains when the fire 
is being forced. The length of flame depends on the amount and 
character of the volatile matter in the fuel, on the rapidity of 
combustion and on strength of draft. It varies from a few 
inches, with coke and anthracite coal, to 8 feet or even more 
with highly volatile coals — even 20 feet has been reached with 
some western coals. 

(f) In order to have complete combustion of all the fuel in a 
furnace it is necessary that uniform conditions prevail through- 
out the fuel bed; and to bring this about it is essential that the 
fuel itself be uniform in character. Therefore, the best results 
are obtained with coal that has been graded as to size. Espe- 
cially is this true with anthracite coal which ignites slowly and 
is more difficult to keep burning than volatile coals. This coal 
requires a rather strong draft and unless the bed is uniform the 
rush of air through the less dense portions tends to deaden the 
fire in those regions, hence good results can be obtained with this 



508 HEAT-POWER ENGINEERING 

coal only when it is uniform in size and evenly distributed. The 
more common sizes of coal are given in Tables XVI and XVII, 
on pages 465 and 466. 

(g) Smoke may be composed of unconsumed, condensible 
tarry vapors, of unburned carbon freed by the splitting of hydro- 
carbons, of fine noncombustible matter (dust), or of a combina- 
tion of these. It is an indication of incomplete combustion, and 
hence of waste, and in certain communities is prohibited by 
ordinance as a public nuisance. Smoke can be avoided by using 
a smokeless fuel, such as coke or anthracite coal; or, when the 
more volatile coals are used, by bringing about complete com- 
bustion of the volatile matter. In general, the greater the pro- 
portion of the volatile content of the coal the more difficult it is 
to avoid smoke, though much depends oh the character of the 
volatile matter. Coals which smoke badly may give from 3 to 
5 per cent lower efficiencies than smokeless varieties. 

For each kind of coal and each furnace there is usually a range 
in the rate of combustion within which it is comparatively easy 
to avoid smoke. At higher rates, owing to the lack of furnace 
capacity, it becomes increasingly difficult to supply the air, mix 
it and bring about complete combustion. Hence when there is 
both a high volatile content in the coal and a rapid rate of com- 
bustion it is doubly difficult to obtain complete and smokeless 
combustion. 

However, although smoke is an indication of incomplete and 
hence inefficient combustion, it may sometimes be more profitable, 
because of lower price or for other reason, to use a coal with 
which it is difficult to avoid smoke, provided the latter is not a 
nuisance or is not prohibited by statute. 

252. Value of Coal as Furnace Fuel, (a) The principal 
factors which determine the commercial value of coal used in 
furnaces are: (i) price per ton, (2) calorific value, (3) moisture, 
(4) volatile matter, (5) ash, (6) clinkering tendency, (7) sulphur 
content, (8) skill and attention required in firing, (9) suitability 
for the furnace and grate in which it is to be used, (10) size of 
coal and (11) available draft. These will be briefly discussed 
in this section. 

(b) As exposure to weather (sun and rain, humidity, etc.), 
during transportation and storage, may affect the amount of 



ACTUAL COMBUSTION OF FUELS 509 

moisture and may also alter the chemical composition and heat 
value of the fuel, especially if rich in volatile matter, the various 
analyses to which the coal may be subjected should be made 
after the coal is received, or as received, if it is desired to deter- 
mine its value to the consumer. The calorific value is preferably 
determined by using a fuel calorimeter (see Sect. 244) ; it may, 
however, be approximated by any of the methods given in Sect. 
227(a) to (d). The moisture, fixed carbon, volatile matter, and 
ash per pound of material may be found by making a proximate 
analysis (Sect. 226(c)). 

(c) If payment is made on the basis of weight of coal " as 
received," and if the heat value is stated per pound of "dry 
coal," part of the expenditure is for an unknown weight of 
moisture and the true value of the coal is unknown. Evidently, 
from the consumer's standpoint, the purchase price should 
depend directly on the calorific value per pound of the moist coal 
as received. In any case the ultimate test of the commercial 
value is the cost per B.t.u. delivered, or the number of B.t.u. 
received for a unit of money expended, other things being equal. 

(d) The moisture in the coal is undesirable as it not only (i) 
reduces the heat value per pound of material fired, but (2) adds 
to the transportation expense per B.t.u. delivered, and this in 
direct proportion to its weight, and (3) decreases the furnace 
and boiler efficiency since it becomes superheated steam, thereby 
absorbing heat (latent and sensible), which is carried up the 
chimney with the flue gases. The heat thus carried away per 
pound of moisture is the same as that per pound of water vapor 
formed from the combustion of hydrogen and is given approxi- 
mately by Eqs. (364) or (365). Roughly, the loss of the total 
heat value of dry fuel is about xV per cent for each per cent of 
moisture present. In eastern coals the moisture normally 
ranges from i to 5 per cent, and in western coals from 3 to 15 
per cent. 

(e) Coals in which the volatile matter is proportionately very 
high usually give very long flames, and cannot be burned com- 
pletely or smokelessly unless used with furnaces of proper type, 
size, and proportions and unless special means are provided for 
regulating the air supply above the grate. Even with the most 
careful management it is usually difficult, and in some cases 
impossible, to obtain complete combustion with such coals even 



Sio 



HEAT-POWER ENGINEERING 



20 30 40 50 60 



% Volatile Matter .in. Dry Combustible 



Fig. 322. 



though an extreme amount of air is used; hence, the calori- 

metric test is not a true measure of the commercial value of such 

fuels in furnaces. Fig. 322 shows in a very general way how the 

efiftciency of combustion varies with 

the percentage of volatile matter in 

g.oD| j 1 — "hs;— j 1 the dry combustible.* 

I >i Coals moderately rich in volatile 

matter, such as semibituminous and 
the less volatile bituminous coals, 
not only have the highest calorific 
values (as shown by the Mahler curve 
in Fig. 315), but, when properly 
fired, generally produce the highest efficiencies of any of the 
coals used, and with suitable conditions and reasonable atten- 
tion can be burned smokelessly, or practically so. 

(f) The ash detracts from the value of coal in a number of 
ways. The greater its percentage the 
more difficult it is to obtain complete 
combustion because of its tendency to 
pack and obstruct the passage of air; 
also the greater may be the proportion 
of coal lost through the grates with the 
ash, and the less is the capacity of a 
given furnace because of the reduction 
of combustible per square foot of grate 
area. The way in which the value of 
the fuel decreases as the percentage of ash increases is shown in 
Fig. 323, which in a general way applies to any kind or grade of 
coal. When the ash constitutes 40 per cent of coal, the fuel is 
practically valueless in ordinary furnaces. 

The expense of generating a given amount of heat is increased 
(l) by the cost of transporting the inert matter in the coal, (2) 
by the transportation and disposal of the ash, (3) by the extra 
labor involved in handling the larger weight of material, (4) by 
the unconsumed coal carried through the grates with the ash 
(which may be from 10 per cent to 60 per cent of the latter), and 
(5) by the heat absorbed by the ash (specific heat = 0.2 to 0.24) 
and carried with it to the ash pit. In commercial coals the ash 



100 


















tii 






"** 




















•^ 


















\ 






.«20 
.10 































\ 


















^ 


CA.B 


erne 


at-" 


Powf 


r" 




y 














\ 














\ 




3 


J 1 


1 


5 2 


2 


5 3 


S 


5 10 



Per Cent Ash in Dry CoaC 

Fig. 323- 



* " Steaming Tests of Coals," Bull. 23, U. S. Bureau of Mines. Page 233. 



ACTUAL COMBUSTION OF FUELS 



511 




Fig. 324. 



generally ranges from 4 per cent to 25 per cent of the total 
weight. 

The smaller the size of coal the more difficult is it to remove 
the inert portion, hence the greater is the proportion of ash 
present, as is shown by curve i in Fig. 324 for one particular 
kind of coal. 

(g) If the ash is fusible at a comparatively low temperature, it 
will form clinkers when a hot fire is maintained, as when the 
capacity of the furnace is being forced. This clinker, of course, 
detracts from the value of the coal. 
Steam, or water vapor, passed through 
the fire with the air, is supposed to 
decrease the tendency to clinker be- 
cause of absorption of heat and the 
consequent lowering of the tempera- 
ture of the ash. For this reason steam- 
blasts are sometimes used under the 
grate with clinkering coals and often 
water is kept in the ash pit to furnish 
vapor. If clinker is formed, the fused 
mass must be frequently broken up to 

permit the free passage of air through the fuel bed to support 
the combustion. 

(h) Sulphur in coal is objectionable not only because of its 
relatively low heat value, but because of the deleterious efifect on 
the boiler materials, and because it is thought that in some 
instances it indicates the presence of clinker-forming matter, 
although clinker also occurs when it is absent. The sulphur 
should not exceed 3^ per cent. 

(i) In general, in using the same coal with a given furnace and 
draft, the efficiency and capacity of a grate will vary with the 
size of the coal, as is shown by curves 2 and 3 in Fig. 324, for one 
particular kind of coal tested under a certain boiler.* The best 
size for given conditions can be determined from experiment or 
from a study of data relating to similar coals burned under like 
circumstances. If for some reason it is necessary to burn a given 
size of a particular coal, there is usually some design of furnace 
and some set conditions which will give best results; these can be 

* Abbott, " Characteristics of Coals," Jour. Western Soc. of Eng'rs., Oct. 16, 
1906, p. 528. 



512 HEAT-POWER ENGINEERING 

determined experimentally if no information on the subject is 
already available. 

In general, the smaller the coal the harder is it to burn com- 
pletely and the greater is the percentage of unburned coal lost 
through the grates with the ash. In consequence there is less 
general demand for the smaller sizes, hence they cost less per ton 
than the larger grades and therefore are widely used in boiler 
furnaces even though their heat value per pound is low because 
of the large percentage of ash present. Very fine coal and dust 
are difficult to burn on ordinary grates as they tend to pack and 
check the flow of air through the fuel bed, or else, with strong 
draft, are carried along with the air to be deposited within the 
boiler setting or to be carried up the stack to become a nuisance 
to the surrounding neighborhood. They may, however, be 
burned successfully by the methods which will be given in Sect. 

253- 

(j) Caking of the coal, if excessive, is in general undesirable 
because of its tendency to prevent the passage of air ; but where 
provision is made to break up the bed, continuously or inter- 
mittently, a certain amount of caking may be advantageous. 

(k) The different kinds of coal, and the various sizes, do 
not generally burn at the same rates under equal drafts. With 
a given grate and draft, it is of course necessary to use a coal 
which will develop the amount of heat that is needed for the 
particular purpose for which the furnace is used, for example, 
if used under a boiler, it must be possible to burn enough coal 
to evaporate the maximum amount of steam required of the 
apparatus. Hence under certain conditions the possible rate of 
combustion may have an influence in the selection of a coal. 
Sometimes when there is uncertainty as to the kind of coal which 
will eventually be used, — the grate is made of such size that the 
heat output will be sufficient even though the slowest burning 
coal is used, — then it will be ample for freer burning kinds — 
and, subsequently, if desirable, portions of the grate can be 
blocked off to reduce its area when the latter are used. 

Further, there is some rate of combustion (pounds of coal 
burned per square foot of grate surface per hour) which will give 
the best combined boiler and furnace efficiency for each kind and 
size of coal. Fig. 325 shows the variation in the case of one 
particular kind and size. In general, the rate and heat develop- 



ACTUAL COMBUSTION OF FUELS 



513 




Lbs.of Coal per Sq.Ft. of Grate Area 



Fig. 325- 



ing capacity of the furnace is least with coals low in volatile 
matter, rich in ash, and small in size, and is, of course, directly 
dependent on the rate of air supply, that is, on the draft. 
The best rate to adopt in each particular instance can be deter- 
mined experimentally, or from a study of similar cases, when 
data are available. 

(1) As the volatile matter is mostly burned beyond the fuel 
bed, the rate at which coal can be burned on a given grate area is 
largely dependent on the proportion of fixed carbon it contains. 
The best economies are usually ob- 
tained when from 12 to 16 pounds 
of fixed carbon are burned per square 
foot of grate surface per hour. The 
ordinary rates of combustion (under 
normal conditions) are about as fol- 
lows: Anthracite, from 15 to 20 
pounds; Semi-bituminous, from 18 to 
22 pounds; and Bituminous, from 24 
to 32 pounds. Dividing the estimated 

total weight of coal which is normally to be burned per hour, 
by the proper normal rate, as here given, results in the necessary 
grate area and allows for an overload capacity of from 50 per 
cent to 100 per cent, depending on the intensity of draft that is 
available. Evidently with anthracite coal there must be a larger 
grate area for a given total capacity than with bituminous coal. 

Greater rates of combustion are possible; for example, in 
torpedo boats under forced draft (4^ inches to 6 inches of water) 
the rate is from 55 to 65 pounds per square foot; and from 80 
to 120 pounds, and even more, have been burned (with air 
pressure of from 4 inches to 8 inches of water). Rates as high as 
90 pounds per square foot per hour are commonly used in loco- 
motive practice where exhaust steam nozzles are employed for 
inducing strong drafts. 

(m) The maximum capacity obtainable with a given furnace 
and with a certain intensity of draft available varies not only 
with the kind of coal but also with the size. Curve 3, in Fig. 
324, shows how it varied with the size of one kind of coal tested 
under a certain boiler. It is to be noted that the maximum 
efficiency is not necessarily obtained with the size that gives the 
greatest capacity. 



514 HEAT-POWER ENGINEERING 

The capacity per square foot of grate area with anthracite coal 
is hmited largely by the fact that if this fuel is burned rapidly, 
it has a tendency to break up into small pieces which pack and 
clog the passage of air through the fuel bed. This action also 
increases the amount of unconsumed coal lost through the grates' 
with the ash and this lowers the efficiency. 

253. Burning Powdered Coal, (a) Powdered coal can be 
burned in much the same way as a liquid fuel (see Sect. (258)) if 
it is finely pulverized and properly injected into a furnace. 
When used in this way it has many of the advantages incident 
to the use of liquid fuel. 

However, the cost of crushing and the difficulty of uniform 
feeding, combined with the complicated apparatus necessary, 
have thus far prevented any wide use of powdered coal as a 
boiler fuel although it has been very successfully and widely 
used for firing cement kilns in regions in which the price of oil 
is high. 

(b) Coal too fine to use on ordinary grates may be briquetted 
by using a suitable binder, as has already been mentioned, and 
can then be used conveniently and efficiently on ordinary grates. 

(c) Where special dumping grates are used with air supplied 
from below, under pressure that can be readily regulated, very 
small anthracite coal has been successfully burned in the following 
manner: The fuel bed is not disturbed for cleaning for several 
hours, the ash being allowed to accumulate; the intensity of air 
pressure in the ash pit is increased as the fuel bed becomes 
thicker, but is always such that it becomes atmospheric at the 
surface of the bed; the products of combustion are carried off 
by draft induced by a stack or other device above the fuel bed; 
and the fuel is distributed as evenly as possible in firing. Owing 
to the fineness of the coal, there is a strong tendency for it to 
burn out in spots, to prevent which the surface of the fuel bed 
must be smoothed very frequently by using a distributing bar 
with a T-head. As the pressure just above the fuel bed is 
atmospheric there is no objection to the frequent opening of the 
doors which is necessary for thus working the fire. Culm and 
other low grade coal, which is ordinarily considered to be waste 
material, may in some instances be burned with satisfactory 
results by this method. 



ACTUAL COMBUSTION OF FUELS 515 

254. Selection and Purchase of Coal, (a) The price per ton 
of the coal deUvered is the sum of the cost at the mines and the 
transportation charges; hence the distance from the mines may 
have an important bearing on the cost to the consumer. The 
cost at the mine depends on the difficulty in mining — hence 
for hard anthracite it is greater than for the softer bituminous, 
coals. Also the price is, of course, dependent on the supply and 
demand. Thus the smaller sizes, being in the least generaE 
demand, are the cheapest per ton at the mine. Grades that are 
generally considered worthless cost least, hence much attention 
is being devoted to devising methods tor utilizing these grades, 

(b) In selecting coal for boilers the problem is to find that 
kind and size which will give the greatest number of useful heat 
units, or which will evaporate the largest weight of water, per 
dollar expended for the fuel and its firing. In default of avail- 
able information on the subject, a series of tests under varying 
conditions may be conducted to determine the coal best suited 
to a given furnace and to find the size of that coal, thickness of 
fire, strength of draft, method of firing, etc., which will give the 
best results under the prevailing conditions. But such tests 
may be as much a determination of the skill of the fireman as of 
the quality of the coal, and, therefore, may not give the true value 
that the coal would have when properly used. Although many 
such tests have been made, the published data of this kind at 
present available are rather meager. 

(c) The principal sources of data are reports of the U. S. 
Bureau of Mines, of State Geological Surveys, Engineering Ex- 
periment Stations, engineering "pocket books," special treatises 
on fuels, combustion, and boilers, catalogs of boiler manu- 
facturers, etc. Nearly all of these reference books give tables 
of the chemical and proximate analyses of the fuels from the 
more important coal fields and while the coals from a given field ,^ 
and even from the same mine, vary considerably in character, 
such data may be used in default of tests of samples of the coal 
actually under consideration. 

(d) Some large consumers have adopted the following plan 
for the selection and purchase of coal: By actual test in their 
furnaces they determine what kind is cheapest and most desir- 
able to use under the prevailing conditions and thus a standard 
specification as to heat value, size, ash, volatile matter, mois- 



5i6 HEAT-POWER ENGINEERING 

ture, sulphur, etc., is drawn up. Then a "standard price" for 
such coal is agreed upon with the dealer, with adjustments 
by premiums and penalties for variations from the specification. 
The adjustment is directly, or almost directly, according to the 
variation in the heat value per pound of the moist coal (or coal 
"as received"), and is dependent on, but not directly propor- 
tional to, the variation in the percentage of ash, volatile matter, 
and sulphur from the standard. 

For example, the Interborough Rapid Transit Company (New 
York City) accepts a run of mine bituminous coal without 
penalty or premium if it contains 20 per cent or less of volatile 
matter, 9 per cent or less of ash, and i^ per cent or less of sulphur. 
The standard heat value per pound is 14,250 B.t.u. with penalty 
and premium averaging about one cent per ton per 50 B.t.u. 
variation from standard. Penalties per ton range up to 18 
cents for 4 per cent excess in volatile matter, and to 23 cents 
for 4I per cent additional ash, and to 12 cents for i per cent 
excess sulphur.* 

Some concerns specify as standard a run of mine, semibitumi- 
nous coal with i per cent moisture, 20 per cent volatile carbon, 
7 per cent ash, and not over i per cent of sulphur. If x is the 
per cent of variation from standard, the adjustment in the price 
is inversely proportional to x for moisture, to 2 x for volatile 
carbon, and to 3 x for ash. 

The government awards contracts on competitive bids which 
-are accompanied by specifications of the kind and composition 
of the coal (ash, B.t.u., and size), which the bidders propose to 
furnish. The analyses are made on the coal "as received," 
which takes care of the effect of moisture. The coal is rejected 
if it clinkers or produces smoke excessively and if it exceeds 
certain limits in the amount of ash, volatile matter, sulphur, 
fine coal, and dust. A small variation from the specified stand- 
ard is tolerated without penalty or premium; but if there is 
much difference, the price is varied directly with the heat value 
of the coal "as received" (including moisture) and is adjusted 
according to a sliding scale for variations in ash and sulphur. f 

* Am. El. Ry. Eng'g. Assoc, Report, 1911. 

t U. &. Bureau of Mines, Bulletin 11, "Purchase of Coal, etc.;" Bull. 41, 
" Results of Purchasing Coal under Government Specifications;" and Technical 
Paper, No. 15, " Sampling Coal, with Specifications." 



ACTUAL COMBUSTION OF FUELS 517 

255. Furnace Operation, (a) The efficiency and capacity 
obtained with a given coal and furnace depend much on the 
knowledge, skill, and attention of the furnace attendant and 
especially is this the case if the furnace is hand fired. 

(b) In addition to the considerations already discussed it is 
important with many kinds of coal to have the right combination 
of thickness of fuel bed and draft. For, in general, with each 
quality and size of fuel, and with each method of firing and rate 
of combustion, there is some combination of thickness and draft 
which will give best results — although there is considerable 
latitude with some coals. Thin beds tend to let an excessive 
amount of air pass through and require frequent and careful 
firing and close regulation of draft. Very thick beds require less 
attention and give quicker response to sudden increase in de- 
mand, but necessitate stronger drafts and are conducive to the 
formation of CO. With a given draft and coal the maximum rate 
of combustion is largely dependent on the thickness of bed. In 
general, the coarser the coal and the stronger the draft, the 
thicker should be the bed. But here, again, it seems impossible 
to give any rule that would be at all general in application; for 
with anthracite coal, the thicknesses used vary from 4 inches to 
12 inches and, with bituminous, from 6 inches to 16 inches, 
depending on the quality and size of coal, the draft, method of 
firing, etc. Hence the best combination must ordinarily be 
found by experience in each instance. 

(c) With anthracite coal not only must the bed be kept uni- 
form but it must be disturbed as little as possible in cleaning 
the fire. Hence shaking grates, which cut off the lower part of 
the bed with minimum disturbance of the upper part, can be 
used to special advantage with this coal. 

(d) The intensity of draft pressure needed is directly dependent 
on the resistance offered to the passage of air through the fuel 
bed. Its pressure is usually stated in terms of "inches of water." 
For the usual kinds and sizes of coal and for ordinary conditions 
the drops in air pressure through the fuel bed are shown by the 
ordinates of the curves in Fig. 326,* in which the abscissas are 
rates of combustion expressed as pounds burned per square foot 
of grate surface per hour. 

* Modified from curves given in "Stirling," publisked by the Stirling Co. (1905). 



5i8 



HEAT-POWER ENGINEERING 



(e) In an up-draft furnace, fired from above, the air ordinarily 
-enters througli the ash doors below the grates, the draft being 
induced by the stack, which in some instances is assisted by 
steam blowers, or by fans. The amount of air and the rapidity 
of combustion can be regulated by adjusting the dampers in the 
flues leading to the stack, by regulating blowers or fans, and by 
varying the openings in the ash doors. If coal is fired inter- 
mittently, as in hand firing, the layer of fresh coal temporarily 



I .20 











/. 


/ 


^ 


k 












^/ 




/ 


/ 














f 


./ 


/ 


/ 




/ 








f/ 




y 

"i 


/ 












/ 5 


w 


f 


4l 


f^j 


^ 


^^\^ 




A 


^ 


y 

^^t 


"bw^ 


^^^v 


5^ 


^^^ 
^^- 




<^ 


/ 


r 




^ 


Sv^ 


:^«o 






t 


1 


1 


5 2 


2 


5 3 


35 4 


D 4 


5 50 



Fig. 326. 



chokes the air supply received through the bed and this occurs 
at the time when the most rapid distillation of volatile matter 
is in progress. Hence, immediately after firing a fresh quantity 
•of coal, particularly if it is rich in volatile matter, an adequate 
supply of air should be introduced above the fuel bed and this 
amount should be diminished gradually as the rate of distillation 
decreases. This air may be furnished through the fire doors, 
which may be gradually closed by hand or by some automatic 
device so arranged that the rapidity of its action can be adjusted 
"to suit the fuel, or it may enter through inlets in the boiler front 
^or in furnace walls, or through passages in the bridge wall at 
the back of the grate. 

In hand firing there is also a loss due to the relatively long 
period of time during which the doors are open while firing, 



ACTUAL COMBUSTION OF FUELS 519 

which permits large quantities of cold air to enter and pass over 
the boiler heating surfaces. As the conditions in the furnace 
vary widely and quite rapidly with the method of firing, the best 
results can only be obtained by close attention on the part of the 
attendants and especially is this the case when the fire is being 
forced — a time when it is the most difficult to give such at- 
tention. 

(f) The way the coal is distributed on the fuel bed is of 
importance. In general, there are three methods of hand firing 
commonly used: 

(i) In one, called spread firing, the fresh coal is each time 
spread evenly over the entire surface of the bed. This is the 
method commonly adopted with anthracite coal. 

(2) In the second, known as alternate firing, fresh coal is 
placed on but one-half of the grate at a time, which permits, 
excess air to pass through the other, thinner and brighter half 
for the combustion of freshly evolved volatile matter. Spot, or 
checker, firing is similar ; alternate spots on an imaginary checker- 
board are fired simultaneously, and, as before, the volatile matter 
from the fresh coal is supplied with heated air by the excess 
amount that passes through the remaining portions of the bed. 
In these methods of firing, the coal is placed each time on the 
brighter portions of the fuel bed. 

(3) In coking firing, which is used only with caking coals, the 
fuel is placed on the front edge of the fuel bed and allowed to 
coke, the volatile matter passing back over the bed and mixing 
with the hot air passing through this portion. After distillation 
is complete the coke is pushed back and distributed over the bed. 
This method, while effective, does not permit of high rates of 
combustion. 

(g) Evidently the best results can be obtained only when the 
conditions are maintained uniform, that is, when the coal is 
fired continuously and uniformly and there is no variation in 
the air supply. Thus, with hand or intermittent firing, the coal 
should be fired frequently, in small amounts, and it should be 
distributed with skill, while, in addition, the draft should be 
carefully adjusted. However, such close attention is opposite 
to the natural tendencies of furnace attendants, and even with 
it, it is impossible with some coals to obtain complete and smoke- 
less combustion with hand firing. 



520 



HEAT-POWER ENGINEERING 



(h) By the use of automatic mechanical stokers, however, the 
coal-feeding operation is made continuous and the conditions are 
kept uniform. They involve but little labor or attention and 
with them it is possible to obtain practically smokeless combus- 
tion with nearly all kinds of coal provided that (i) the grates and 
the furnace setting are properly proportioned to suit the fuel, 

(2) proper attention is given to the firing and air supply, and 

(3) a suitable rate of combustion is used per square foot of grate 
surface. Mechanical stokers will be described in Sect. 257. 

256. Grates and Furnaces, (a) The number of square feet 
of grate surface may be determined in the manner described in 
Sect. 252 (1). The width of grate is commonly made equal to the 
distance between the walls of the boiler setting, and the length 
of grate is ordinarily found by dividing the desired area by this 
width. With hand firing, grate lengths up to 10 feet have been 
used with dumping grates, while with ordinary grates the limit 
of length is usually 6 feet because of difficulty in cleaning the fire. 




^ W 



Fig. 327. 



(b) To prevent the grate bars from burning away they should 
be of suitable material (white C. I. is generally used), and should 
be of such shape as to present relatively small surface to the fuel 
bed and expose large radiating surface to the current of air. 
They must be in short lengths (not over 3 feet ordinarily), set 
so as to allow for expansion and contraction and also for warping. 
They must provide sufficient passage for air, and must permit 
the ash, but not the coal to pass through. In addition they must 
be readily cleaned of clinker. 

(c) Of the great many kinds of grate bars in use four of the 
most common forms are shown in Fig. 327. In this figure, (c) 



ACTUAL COMBUSTION OF FUELS 



521 



is for sawdust and the rest are for coal. For fine coal flat plates 
like (d) with small perforations are sometimes used; and these 
may have the exposed surface recessed so as to become filled with 
a permanent layer of fine 
ashes in order to protect the 
bar from the heat and also 
to prevent the adherence of 
clinker to the metal. 

(d) Fig. 328 shows one 
form of shaking grate, of which 
there are a great many dif- 
ferent kinds in use. With 

such grates the fire is not only more easily cleaned, but the fire 
doors do not have to be opened during the operation; and the 
bed is disturbed but little, which is especially valuable when 
anthracite and noncaking coals are burned. Some are provided 
with means for breaking the clinker, or the caked coal bed, and 
others for dumping. Their cost is, of course, greater than for 
ordinary grates but they often give from i per cent to 5 per 
cent better efficiency than flat grates. 





Fig. 329. 

(e) Fig. 329 shows a typical furnace with fittings. The 
arrangement shown in Fig. 330 is the roofless furnace suitable for 
coals low in volatile matter, say with less than 20 per cent. 
Fig. 331 shows the tile roof arrangement in which the flame is 
protected by a roof of refractory material supported by the 



522 



HEAT-POWER ENGINEERING 



lowest row of boiler tubes. This arrangement is suitable for 
long flame coals, for ordinarily there is little difficulty in making 
the roof at least as long as the flame. 

(f) Fig. 332 shows a Dutch oven which can be built in front of 
any type of boiler. It offers an incandescent roof and walls to 





Fig. 33°- 



Fig. 331- 




reflect the heat and makes possible the complete combustion of 
volatile matter, but it adds to the radiation losses because of the 
increased surface exposed. When possible it should be confined 
within the regular boiler setting, so as to reduce this external 
surface. In the Dutch oven the roof and walls are sometimes 
made double with passages between for the circulation of air 

which is supplied to the furnace. 

( I I f This arrangement serves the 

_SJL-^ i^^^^S double purpose of furnishing hot- 

ter air and of reducing the radia- 
tion loss by lowering the temper- 
ature of the outer walls. 

(g) In all these figures of fur- 
naces the distance A should at 
least equal the flame length, and the external radiating surface of 
the setting should be made as small as is expedient. The fur- 
naces and passages for the hot gases must be lined with fire brick, 
using only the best grades in furnaces in- which the firing is 
forced. Baffle arches, piers, wing walls, etc., are sometimes 
introduced in the passageway of the gases to mix them and 
perfect the* combustion. 

(h) Fig. 333 shows a down-draft furnace. In this form of 
furnace the upper grate bars are cooled and are rather widely 
spaced. The coal is fired on the upper grate and the volatile 
matter is carried downward by the draft so as to pass over the 
hot, partly burned coals which have fallen to the lower grate. 



Fig. 332- 



ACTUAL COMBUSTION OF FUELS 



523 




(i) The efficiency of a grate is, of course, lowered by the loss 
of unburned coal with the ashes, while that of the furnace is de- 
pendent on the completeness of combustion and on the radiation 
from the external walls. As these efficiencies have an intimate 
bearing on the performance of 
the boiler, they will be con- ji\\l 
sidered in connection with the 
general discussion of boiler ef- 
ficiencies in Sect. 259. 

257. Automatic Mechanical 
Stokers, (a) The principal ad- 
vantages derived from the use 
of mechanical stokers are: (i) Continuous firing and uniform 
conditions; (2) progressive distillation of volatile matter and 
proper provision for burning it; (3) a saving of from 30 to 40 
per cent labor cost in large plants (in small plants there may be 
no saving because a certain number of firemen are always neces- 
sary and the introduction of stokers may not reduce the number) ;; 
(4) relief of men from strenuous duties and from exposure to 
heat; (5) greater ease in obtaining good economy; (6) the elimi- 
nation to a large extent of the personal element in firing; (7) the 
greater possibility of smoke prevention with the poorer grades 
of coal; and (8) greater rates of combustion than are possible 
without smoke. 

(b) The main disadvantages (which may, or may not, be pres- 
ent in any given make of stoker) are: (i) Greater first cost (and 
interest on same); (2) possible lack of durability and greater 
cost of repairs ; (3) cost of power to operate ; (4) greater compli- 
cation; (5) inability to meet sudden changes in load; (6) failure 
to distribute coal evenly; (7) loss of unburned coal with ashes; 
and (8) loss due to use of steam in the air-blast. What was 
said about the design and arrangement of grate bars and furnaces 
in general in the preceding sections also applies to automatic 
stokers. 

(c) At the lower rates of combustion it is possible to obtain, 
about as good results with hand firing as with automatic stokers,, 
but this involves the employment of painstaking men of great 
skill who command higher wages than the ordinary. With 
automatic stokers and furnaces designed to suit the coal and 



524 



HEAT-POWER ENGINEERING 



draft, the best results are obtainable with very little effort or 
skill on the part of the attendants. Most plants using auto- 
matic stokers are also equipped with automatic coal conveying 
machinery and means for delivering the coal by gravity to the 
hoppers of the stokers, and in such cases the labor is, of course, 
reduced to a minimum. 

(d) No one type of mechanical stoker is equally valuable for 
all kinds of coal, but practically any kind of coal can be burned 
efificiently and smokelessly with a suitable stoker, provided the 
rate of combustion does not exceed a certain value which is 
dependent on the kind of coal.* 

(e) In hand firing one man can effectively attend to from 200 
to 500 boiler horsepower, and at the same time wheel the coal 
and ashes, and regulate the feed water pumps, draft, etc. In 
such case from 1000 to 2500 pounds of coal are handled per hour. 

When merely firing, with coal delivered by others, one man can 
hand fire about 1000 boiler horsepower, i.e., handle from 4000 
to 5000 pounds of coal per hour. 

With automatic stokers provided with coal fed by gravity 
from overhead bunkers, one attendant 
can ordinarily care for from 2000 to 
4000 boiler horsepower, using from 
8000 to 20,000 pounds of coal per hour. 
(f) Mechanical stokers may in gen- 
eral be classified as: 

(a) Over feed (including (i) front 
feed, (2) side feed, and (3) chain grate) 
and (b) under feed. 

These will now be discussed in a very 
general way. 

(g) In most over-feed stokers (see Fig. 334) the coal is deposited 
in a hopper from which it is automatically and continuously fed 
to the grate and made to pass under a more or less extensive 
coking arch, which is maintained at a high temperature and serves 
the same purpose as the roof of the Dutch oven. Air, heated or 
otherwise, is usually admitted with the coal under the coking 
arch. The grate bars are moved in such manner as to carry the 
bed of coal constantly in one direction and as it progresses it 

* Bull. 40, U. S. Bureau of Mines, " Smokeless Combustion," an investigation 
of several hundred plants. 




Fig. 334. 



ACTUAL COMBUSTION OF FUELS 525 

gradually burns out. As the coal approaches the hotter portion 
of the fuel bed a progressive distillation of the volatile matter 
occurs. The resulting gas mixes with the air above and the 
mixture then passes under the coking arch which, being heated 
to incandescence, reflects the heat from the bright portions of 
the bed and deflects the gas so as to make it pass over the rest 
of the bed. Thus the conditions are excellent for the complete 
combustion of the volatile content. 

The rate at which coal is fed from the hopper to the grates and 
at which it is carried along the latter can be varied and should be 
so adjusted that combustion of the coal is just completed when 
the end of the grate is reached. If completed before this point 
cold air will force its way through the thin bed of ashes at the end 
and reduce the efficiency; and if not completed unburn ed coal 
will be lost with the ashes. 

The stokers may be driven in various ways, such as by small 
steam engines, by electric motors, or by belting from conveniently 
located line shafting. 

(h) Fig. 335 shows diagrammatically a typical arrangement 
of a front-feed stoker with inclined grate. It has a hopper, coal- 
pusher feeding-device, dead plate, coking arch, and air inlet 
under the latter. The grate bars are stepped and inclined, and 
they are mechanically oscillated, or reciprocated, in such way 
as to cause the bed of coal to gradually descend. The rapidity 
and amplitude of motion of the pushers and grates can be so 
regulated that the coal is just burned out by the time it reaches 
the bottom of the grate. The ashes and clinker become de- 
posited on the ash table, which is dumped by hand from time to 
time. When the ash table is tilted a guard is brought into 
position (as is shown at (a) in the figure) to keep the fuel bed 
from sliding down and being dumped at the same time. In the 
figure, the upper reciprocating grate bars are hollow and the air, 
which is injected into their interiors by steam jets S, issues 
through openings in the risers of the steps. The lower grates 
rock or oscillate about the trunnions shown in (b) and have 
replaceable bars. There are, of course, many other designs and 
arrangements of front-feed stokers. 

(i) The typical arrangement of side-feed stokers is shown 
diagrammatically in Fig. 336. Coal is fed into the magazine 
from above or through doors (a) in the front and is pushed, by 



526 



HEAT-POWER ENGINEERING 



^^>. DUMPING 

'^^^--^^^^ priQITlOM 





1( Motor) 



Fm 


^ i 
I 


^ 


rf 


3 ^ 
3 




^ 




pt 


I 




.,///;/ 


////// 


////////^ 



•////////m/M/Ji} 



Fig. 336. 



ACTUAL COMBUSTION OF FUELS 



527 



some suitable mechanism, to the coking plate at the top of the 
inclined grates. The whole bed of fuel is covered by a fire-brick 
arch, and air, which is heated by passing over the arch, is dis- 
charged into the furnace just above the entering coal. The coal 
gradually descends on the inclined grate bars, the alternate ones 
of which are constantly moving. The ash and clinkers are 
crushed by rotating (or reciprocating) grinders located at the 
bottom of the grates. Some grinders are made hollow and are 
connected to the draft in such way as to cause cold air to pass 
through them to prevent overheating. When clinkering coal 
is used, steam (from the stoker engine, if there is one) is dis- 
charged through the bed of ashes to reduce the amount of clinker 
and to make crushing easier. 




Fig. 337- 



The advantageous features of this type of stoker are the large 
coking spaces, the ample coking arch, and the voluminous com- 
bustion chamber. These stokers operate successfully with both 
uniform and variable loads and under a great variety of condi- 
tions. With some, when certain types of coal are used, there is 
difHculty in getting rid of the ash and clinker. The types differ 
principally in the manner of feeding the coal and getting rid of 
the residue. 

(j) The typical arrangement of chain-grate stokers is shown in 
Fig- 337- This has the hopper, the coking arch with air ducts 



52^ 



HEAT-POWER ENGINEERING 



and the feeding device common with the other forms of over-feed 
stokers already described. The grates consist of a series of 
endless chains carried on sprocket wheels which slowly rotate 
and thus carry the coal toward the back of the grate. The whole 
mechanism is usually mounted on wheels on a track and can be 
pulled forward for inspection or repairs. These stokers are 
particularly adapted to the smaller and poorer grades of non- 
caking coals. To operate satisfactorily the thickness of fire, 
the draft, and the speed of the grate must be adjusted to suit the 
load. Combustion should be complete when the coal has just 
reached the back of the grate. 

(k) In the under-feed stokers, a typical arrangement of which 
is shown in Fig. 338, the coal is fed forward from the hopper, by a 




Fig. 338. 



reciprocating pusher, as shown (or by a screw conveyer or other 
suitable feeding device), into a retort, around the upper edges of 
which are replaceable tuyere blocks, through which air is supplied 
under pressure. The combustion takes place at the top of the bed 
towards which the fresh coal is fed from below. The ashes and 
clinkers fall to the sides of the retort on dead plates from which 
they can be readily removed through doors in the furnace front. 
The volatile matter is liberated as the coal becomes heated and 
this must pass through the intensely hot coals above, where it is 
mixed with the entering air and is completely burned. Even 
with volatile coals, the combustion is completed within a very 
short distance from the surface of the fuel bed, hence only a very 
short combustion space is necessary. Such stokers give satis- 



ACTUAL COMBUSTION OF FUELS 529 

factory results even when placed in corrugated flues as small as 
three feet in diameter, such as are used in internally fired boilers. 

With such stokers it is necessary to use very strong draft 
(about three inches of water) which must be furnished by some 
forced draft system, hence the operation is independent of 
weather conditions. In some instances the rate at which air 
and coal are supplied is controlled automatically by the steam 
pressure. In one such arrangement the speed of the blower- 
engine is regulated by the steam pressure (a drop in pressure, due 
to a sudden demand on the boiler, causing an increased speed and 
hence a greater delivery of air) and the valves for the steam- 
actuated coal feeder are operated by this same engine ; hence the 
rates at which the air and coal are supplied are changed 
simultaneously, are kept properly balanced, and the boiler pres- 
sure is automatically maintained substantially constant. 

With these stokers it is possible to obtain very high rates of 
combustion in a very limited space, from 500 to 600 pounds of 
coal per hour being consumed in each retort. They operate 
best with bituminous coals which are low in ash and they are not 
ordinarily satisfactory with fine anthracite coals.* 

There are, of course, numerous possible arrangements of such 
stokers. In some the retorts are inclined and have two hori- 
zontal pushers, one above the other. 

258. Burning Liquid Fuel, (a) Both crude petroleum and the 
product of its partial refinement, fuel oil, are very extensively 
used as fuel in boiler plants. The fuel oil is generally preferable 
to crude petroleum on the score of safety as, due to the removal 
of the more volatile constituents during the refining process, 
its flash point is higher. Most fuel oil also has a lower water 
content than the crude material and for this reason there is less 
danger of the flame being extinguished by water collecting in 
the fuel pipes and then passing as a "slug" through the burner. 

(b) To successfully burn fuel oil it is necessary to spray, or 
"atomize," it very effectively and to mix this in the furnace with 
the necessary air. The furnace should be well lined with brick 
which, becoming incandescent during operation, will insure 
satisfactory combustion so long as there is sufficient air well 
mixed with the fuel. It is also essential that the furnace be so 
large and so shaped that the burning fuel does not come in con- 
* Bull. 40, U. S. Bureau of Mines. 



530 



HEAT-POWER ENGINEERING 




Fig- 339- 




Fig. 340. 




Fig. 341- 



By-pas6 of Heater 




Fig. 342. 




ACTUAL COMBUSTION OF FUELS 



531 



tact with boiler heating surface ; failure in this respect will result 
in incomplete combustion of the fuel, as in the case of long 
flaming bituminous coal, and is also liable to result in the over- 
heating and ultimate failure of the exposed heating surface. 

(c) The oil is generally atomized or sprayed by compressed 
air or by steam, the latter being now the more common method. 
It is also occasionally atomized mechanically. In most cases the 
oil is pumped from storage tanks to burners by small steam- 
driven pumps. On the way to the burners it is heated by means 
of the exhaust steam from the pumps, after which it enters the 
nozzles or "burners," from which it is so sprayed as to give a long 
jet of finely divided fuel which can thoroughly mix with air 
admitted to the furnace. The amount of steam required in 
handling the oil varies from about 2.5 per cent to 5 per cent of 
the total amount generated — usually it is about 3 per cent and 
is about evenly divided between the pumps and the burners. 




Fig. 344- . Fig. 345- 

(d) The principal advantages of burning oil under boilers are: 

1. Ease of handling from tank car to furnace, as no man- 

ual labor is required even in the smallest plants. 

2. Small weight and volume, since the oil has 30 per cent 

higher calorific value for equal weight, as compared 
with coal. 

3. Lack of clinkers and ash. 

4. Higher average operating efHciency because of (a) ease 

of operation, (b) ability to properly gauge and main- 
tain necessary air supply, (c) smaller excess of air 
required because of ease of forming good mixture, and 



532 HEAT-POWER ENGINEERING 

{d) more uniform furnace conditions because there is 
no necessity to open doors at frequent intervals. 

5. Practical elimination of soot and smoke. 

6. Decreased labor bill in large plants because of ease with 

which one man can handle several thousand boiler 
horse power. 

7. Ease with which boiler can be made to follow rapid 

fluctuations of load. 

(e) To offset these advantages are high cost of oil fuel in 
comparison with coal in many parts of the country and the 
increased danger of fire due to the more inflammable character 
of the fuel. 

(f) Figs. 339, 340, and 341 show several burners, of which 
there are a great many other forms in use. One of the numerous 
possible arrangements of the oil-feeding system is shown in 
Fig. 342; and in Figs. 343, 344, and 345 are illustrated three of 
the many arrangements of furnace in use, 



CHAPTER XXX. 
BOILERS. 

259. Losses Connected with Steam Generation, (a) Be- 
cause of the very intimate connection between the boiler proper * 
and the other parts which make up the steam generating appara- 
tus, it is most convenient to discuss the losses and efficiencies of 
boiler, furnace, and grate at the same time. Reference to the 
energy stream in Fig. 346 will assist in following the discussion. 

(b) It should first be observed that it is the function of the 
furnace to receive fuel, with its supply of heat in latent form, 
and to make the maximum possible amount of this heat avail- 
able for use. The furnace may therefore be called the " heat 
generator." It is then the function of the boiler proper to serve 
as a " heat absorber " and to transmit to the contained water 
and steam as large a part of this heat as possible. But losses 
always occur in making the heat available in the furnace and 
similarly there are some that are unavoidable in utilizing that 
heat. 

There are in general three losses in the furnace: (i) Some of 
the combustible is not burned, but is lost with the ash; (2) 
some, which is not so lost, is incompletely burned and passes off 
with the products of combustion in fine particles; and (3) some 
of the heat actually made available in the furnace is lost by 
radiation and cannot therefore be utilized by the boiler. 

Thus, only a fraction of the heat originally supplied with the 
fuel is really brought to the boiler heating surfaces for utilization 
and part of this must always be unavailable even in an ideal 
boiler, for after the products of combustion are cooled to the 
boiler (steam) temperature there can be no further transfer of 

* The term " boiler " is ambiguous. It is used to refer to the boiler proper (or 
vessel containing the water and steam) and also to this element in combination 
with the furnace, setting and other parts, which collectively comprise the whole 
steam generating apparatus. However, this should not lead to confusion as the 
context always makes clear the sense in which the term is used. 

533 



534 



HEAT-POWER ENGINEERING 



heat to the boiler.* This unpreventahle loss is equal to the heat 
required to raise the temperature of the flue gases from atmos- 
pheric to boiler temperature. 

Including this one there are three losses of heat associated 
with the boiler proper or " heat absorber." These boiler losses 
are: (i) The unpreventable loss (in the ideal case) equal to 
the heat utilized in raising the flue gases to boiler temperature; 
(2) a loss resulting from the fact that in commercial boilers 
the temperature of the flue gases is never reduced to that of the 
steam ; and (3) a loss resulting from the radiation from external, 
surfaces of boiler and setting. 




(1) Combustible 



(5) Stack loss above "^ -t^ a 

1 Steam Temp. / J23 

}*(« Heat used in )-i| 

-° raising flue gases Vijfri 

^ to temp.of steam 1 Wo 



Combustion 

Fig. 346. 

The exact values of the total radiation loss of the complete 
apparatus and the proportions chargeable separately to furnace 
and to boiler are generally indeterminate, but they may be 
approximated more or less closely in some instances. 

(c) During a boiler test, it is possible to obtain data which 
can be used in determining the distribution or destination of the 
known heat value of the fuel actually fired. The tabulation of 
such information is called a heat balance and accounts for all 
the heat utilized and lost. It is usually stated both in terms 
of B.t.u.'s and on the percentage basis. A complete heat balance 
would include the following eleven items: (i) The heat utilized 
(absorbed by the water heated and the steam generated) ; the 

* There is an exception to this statement in the special case of boilers that 
operate on the "counter flow principle." This will be discussed later. 



BOILERS 535 

losses due (2) to unconsumed combustible in the ash and (3) 
to the removal of ash from the ash pit while at high tempera- 
ture; the stack losses (Sect. 248) occasioned by (4) moisture in 
the fuel, (5) humidity in the air supplying the oxygen, and (6) 
water formed by the combustion of hydrogen, and that due to 
(7) the sensible heat in the flue gas; the losses due to (8) uncon- 
sumed CO, (9) unburnt hydrogen and hydrocarbons and (10) 
to the solid fuel (such as fine coal dust and soot) carried off by 
the draft; and (11) the losses not otherwise accounted for — 
principally radiation. The sum of the items on the B.t.u. basis 
must, of course, equal the heat in the coal actually fired, and 
on the percentage basis it must total 100 per cent. 

(d) In real tests it is seldom practicable to make any such 
complete balance as that just given. It is common practice * 
to limit it to the following six items: — (i) Heat absorbed by the 
boiler proper and the losses due to (2) moisture in the coal, 
(3) moisture formed by the burning of hydrogen, (4) sensible 
heat in flue gases, (5) unconsumed CO, and (6) those not other- 
wise accounted for (including that due to unconsumed H and 
hydrocarbons, moisture in air, radiation and others not listed 
above) . 

A complete discussion of the method of determining the vari- 
ous losses is outside the province of this book. For further 
details the student is referred to books devoted to Boilers and 
Furnaces and to Experimental Engineering. 

260. Efficiencies Connected with Steam Generation, (a) 

After the preceding discussion of the losses occurring in boilers 
and after a study of the energy stream in Fig. 346, it is evi- 
dent that numerous ratios between the widths of the stream at 
various points will give efficiencies of the different elements of 
the steam generating apparatus and of their combinations. The 
more important of these efficiences will now be given, but as 
they are clearly shown in Fig. 346 the discussion will be very brief. 
(b) Of the combustible placed in the furnace, a part may be 
lost through the grates with the ash. That which is not thus 
lost must ascend from the grate as volatile combustible, as 
gaseous products of combustion, as unburnt solid matter, or as 
a mixture of these; it will be called "combustible ascending 

* Rules for Conducting Boiler Trials. Code of 1899, Trans. A.S.M.E., 1899. 



536 HEAT-POWER ENGINEERING 

from the grate " or " ascending combustible." Obviously, the 
Grate Efficiency is 

„ , _ Weight (or heat value) of ascending combustible , . 
Weight {or heat value) of combustible fired ' " 

which is shown in Fig. 346 by the ratio CD/CE. 

(c) The Efficiency of the Combustion Space (including the 
coking arch, gas mixing structures, and other parts of the furnace 
above the grate) is 

„ , _ Heat made available for absorption by boiler , . 
Heat in ascending combustible ^ 

This is shown in Fig. 346 by the ratio FG/ FH. 

(d) The furnace, or " heat generator " includes both the grates 
and the combustion space. Hence the Furnace Efficiency is 

-R-Rf — ^^'^^ made available for absorption by boiler , , 
Heat value of combustible fired 
= GEf X CEf (401a) 

In Fig. 346, FEf is the ratio IJ/IK. 

The numerator in Eq. 401 is evidently equal to the sum of (i) 
the heat absorbed by water and steam, (2) the heat in flue gases 
leaving boiler and (3) the radiation from the boiler and its walls. 
Items (i) and (2) can be determined without difficulty, but the 
radiation losses can in general only be approximated. For this 
reason the Furnace Efficiency is often omitted from reports of 
tests. 

(e) It has been seen that the heat used in raising the flue gas 
from the temperature of the atmosphere to that of the steam 
is not ordinarily available for use in the boiler proper; * hence, 
if the products of combustion are at a temperature equal to, or 
below, that of ebullition there will be no heat used by the boiler, 
even though the furnace itself has high efficiency, — and as far 
as the boiler proper is concerned, all of the heat is then wasted. 
To have the boiler use the maximum amount of heat evolved, 
the unavailable portion must of course be made as small as 
possible. This useless amount is not only dependent on the 
temperature difference between the air and steam, but also on 
the weight of the gas heated. It can, therefore, be minimized 

* See footnote on page 534 for exception. 



BOILERS 537 

by decreasing the weight of excess air suppHed for combustion. 
Furthermore, the benefit of such reduction is twofold, for not 
only does it decrease the amount of heat unavailable, but it 
results in higher temperature of the products of combustion, 
which makes the unavailable portion a smaller percentage of the 
total heat evolved, which in turn increases the efficiency of the 
steam generating apparatus as a whole.* 

(f) The Apparent Efficiency of Boiler (alone) may be defined 

as 

. „ „ . Heat absorbed by water and steam , , 

ABEf = ,, ^ , — 7 u J • ^ ■• • (402) 

Heat developed in furnace 

and in Fig. 346 ABEf = LM/LN. The determination of this 
efficiency involves a knowledge of the furnace losses, - — hence, 
like the Furnace Efficiency, it is difficult to determine accurately. 

(g) But some of the heat developed in the furnace has been 
shown to be unavailable for the ordinary boiler, and it is hardly 
just to charge against such a boiler the non-utilization of this 
portion; hence, the apparent efficiency is not a true measure of 
the performance in such case. Calling the heat with tempera- 
ture above that of the steam "potential heat," then, what maybe 
termed the True Boiler Efficiency is, evidently, 

Heat absorbed by water and steam , , 

^^^^^ Potentialheat ' ' ^^os) 

In Fig. 346, TBEf = OP/OQ, the unavailable heat being shown 
hy QR. 

(h) What is called " Boiler Efficiency " in the A.S.M.E. code f 
applies to the combined efficiency of boiler proper and combus- 
tion space and is expressed as follows: 

■ur'Rf — Heat absorbed by water and steam , , 

Heat available in ascending combustible' 
= ABEf X CEf (404a) 

* It has been suggested (Bull. 23, U.S. Bureau of Mines) that the numerators 
in Eqs. (400) and (401) should include only the heat above the steam temperature. 
However, while this limitation would be satisfactory for comparison between boilers 
of the ordinary type, it would be inapplicable to those using the "counter flow" 
principle. Hence, in this text, the numerator will be taken as the total heat evolved 
in the furnace, regardless of its temperature. 

t Trans. A.S.M.E., 1899. 



538 HEAT -POWER ENGINEERING 

In Fig. 346 BCEf = ST/SU. This efficiency measures the 
perfection of operation of the boiler and combustion space com- 
bined (not including the grate) and as it can be readily deter- 
mined it is generally given in reports of boiler tests. 

In practice " Boiler Efficiencies " as high as 85 per cent have 
been obtained with oil fuel in short tests under exceptional con- 
ditions. In continuous running, 75 per cent efficiency with coal, 
and 80 per cent with oil, are attainable under uniform conditions. 
With variable loads and ordinary conditions, average efficiencies 
of 60 to 65 per cent throughout the year represent good perform- 
ance. 

(i) The Overall Efficiency (OEf = VW/ VX in Fig. 346) includes 
the Grate Efficiency as well as the " Boiler Efficiency," and in 
the A.S.M.E. code is termed the " Efficiency of boiler including 
grate." It is a measure of the perfection of the combined per- 
formance of the boiler, furnace, and grate, and is affected by the 
skill of the firemen, the suitability of the coal and draft, the 
dropping of coal through grate bars, etc. Hence 

„ Heat absorbed by water and steam , , 

Heat in the combustible fired 
= BCEf X GEf = GEf X CEf X ABEf. . . (405a) 

The OEf can be readily determined and hence is usually incor- 
porated in reports of boiler tests. With solid fuels its numerical 
value is slightly less than the BCEf. 

(j) Except in the case of " Boiler Efficiency " (BCEf) and of 
" Boiler Efficiency including grate " (OEf), there is lack of agree- 
ment among engineers as to the definitions and names of the 
efficiencies of the various elements of the steam generating 
apparatus. Hence, before proceeding with the discussions 
including the use of such terms it is always important to first 
arrive at an understanding of their meanings. The terms and 
definitions used in the foregoing treatment appear to the authors 
to be the most satisfactory ones. 

261. Boiler Heating Surface and Heat Transmission, (a) 

The water heating surface (H.S.) of a boiler is the surface of 
those parts of the shell which are in contact with water on one 
side and with the furnace gases on the other. As the transmis- 
sion of heat from the flue gases to the boiler shell is less rapid 



BOILERS 539 

than that from the shell to the water, the heating surface should 
theoretically be measured on the gas side of the plates or tubes. 
In the case of tubes, however, it is common practice to consider 
the outer (larger) surface as heating surface, regardless of 
whether it is exposed to water or gases. 

(b) With a given amount of potential heat in hot gases, the 
more extensive the heating surface the nearer will the flue gases be 
cooled to boiler temperature and, neglecting radiation, the higher 
will be the true efficiency of the boiler. 
This is shown by curve E in Fig. 347 
where ordinates are efficiencies, or 
relative performance, and abscissas 
are extent of H.S. With infinite sur- 
face all the potential heat would be 
absorbed and thus this efficiency 
would be 100 per cent on this assump- pj y_ 

tion. However, it is, of course, neces- 
sary to include the effect of the radiation losses which evidently 
depend directly on the extent of the radiating surface which is 
proportional to the heating surface. In Fig. 347 the percentage 
of this loss is represented by the ordinates of the line R. The 
net result, or percentage of heat usefully utilized, is given by the 
difference between the ordinates of the two curves and is shown 
by line E-R. Evidently the maximum efficiency, considering 
radiation, occurs when the boiler heating surface has an extent 
represented by the abscissa OM. 

(c) Since the cost of boiler, together with that of its floor 
space and housing, increases with the extent of heating surface, 
and since the interest on first cost plus the amount set aside 
yearly for depreciation, insurance and taxes also increases at 
the same rate, there is also a commercial reduction in value with 
the extent of surface, which may be shown by some line such as 
C in the figure. Hence, the true or commercial value of the heat- 
ing surfaces would be shown by some such curve as E-R-C, 
and the maximum value corresponds to a heating surface shown 
by OM' . Either greater or smaller amounts of heating surface 
would give less return per dollar expended, hence the extent of 
heating surface should correspond to this abscissa. 

(d) The mean rate of evaporation per square foot of heating 
surface per hour for the whole boiler is obtained by dividing the 



540 



HEAT-POWER ENGINEERING 



]!8 


3 




_(.!-)- 




















=^ 


^ 


N 








11 

10 
9 


■ 


r>rr 


si 


^ 






\ 


^ 


\ 






fi 












^ 


^ 




S 














^ 


V 


7 


° 
















w 




L 




i 


. 












TI.E. per Sq. Ft. H.S. per Hr. 

Fig. 348. 



total weight of equivalent evaporation per hour by the total 
heating surface. From data obtained from tests of many boilers 
operated at different rates, points may be plotted with abscissas 
representing these mean rates of evaporation and with ordinates 
representing either efficiencies or Units of Evaporation per 
pound of combustible per hour. Average curves drawn with 
respect to such points resemble those shown in Fig. 348 * and 

are seen to be similar to E-R in 
Fig- 347- They indicate that the 
maximum efficiency occurs when 
the "equivalent" mean rate of 
evaporation for the whole boiler is 
between 2 and 4 pounds per square 
foot per hour, corresponding ap- 
proximately to a transmission of 
from 1900 to 4000 B.t.u. per 
square foot per hour. 

(e) But all parts of the heating surface are not equally effec- 
tive. Evidently those parts in the direct path of the*gases are 
of greater value than those exposed merely to stagnant gases, 
and those nearest the source of heat are the most efifective of 
any. Heating surface exposed to the "radiant" heat of the fuel 
bed and burning gases is very much more effective than that not 
so exposed. Thus, in some cases, the small heating surface 
immediately over the fire may transmit as much as two-thirds 
of the total heat absorbed by the boiler, and at this point from 
20 to 35 or more pounds of water may be evaporated per square 
foot of heating surface per hour, whereas the average for the 
whole boiler may not be more than one- tenth as much. It 
follows that surfaces farthest away from the furnace must neces- 
sarily transmit very much less than the average. Hence impor- 
tance should be placed not only on the amount of heating surface 
but also on its distribution and location. 

(f) Without going into a detailed discussion of Heat Trans- 
mission at this point (for this will be given in Chapter XXXV) it 
will be advantageous to mention here the manner in which the 
heat generated in the furnace is transmitted to the steam. 

Briefly, the heat from the fuel bed is first brought to the heat- 

* Such curves are given in Kent's "Steam Boiler Economy" and in Donkin's 
"Steam Boiler Performance." 



BOILERS 541 

ing surface by direct radiation from the glowing coal and burn« 
ing gases (i.e., as " radiant " heat), and by convection by the 
gases which come from the furnace; it is then passed through 
the metal walls by conduction, to be absorbed by the water which 
may also transport it by convection due to the circulation of 
this liquid; and finally, when the water has reached the tem- 
perature of ebullition, the further addition of this heat results 
in the formation of the vapor. 

(g) The rate of transmission * per unit of area of heating 
surface depends, among other things, on (a) the difference in 
temperature between the transmitting and the receiving media; 
{h) the rapidity (velocity) with which the gases are brought in 
contact with the heating surface, and (c) the rapidity with 
which the heat can be carried away by the water (rapidity of 
water circulation) ; {d) the amount of scale and grease on the 
water side of the plate, and {e) the amount of soot on the surfaces 
exposed to the flue gases. 

(h) The effectiveness of each part of the heating surface is 
dependent, among other things, on the difference between the 
temperature (/;,) of the gases on the one side and that {tw) of the 
water on the other, i.e., on {tg — tw) ■ In the case of the ordinary 
boiler, as has been shown, tw is constant and equal to the tem- 
perature of the steam, since all the water is (approximately) at 
that temperature. As the gases progress over 
the heating surface this temperature differ- 
ence diminishes and the heat transmission per 
square foot becomes less until the limit of 
effectiveness is reached, which generally occurs 
when the temperature difference has been re- 
duced to around 100° to 200° F. 

(i) There is, however, one way of obtaining 
a value of tw that is below the steam tempera- 
ture and therefore of making it possible to 

absorb more of the heat from the flue gas t-. 

Fig. 349. 
than can be accomplished in the ordinary 

boiler ; this involves the use of counter current flow. The prin- 
ciple under which this operates can be explained in connection 
with Fig. 349, in which the arrangement is such that the pump 

* Reference, U. S. Bureau of Mines, Bull. 18, "The Transmission of Heat into 
Steam Boilers." 




542 HEAT-POWER ENGINEERING 

forces the water downward through the heating coils, whereas 
the hot gases pass upward — that is, the heat-conveying and 
heat-absorbing media flow in opposite directions. With such 
arrangement it is obvious that the addition of more heat absorb- 
ing coils at the top (as shown dotted) will result in lowering the 
temperature at which the gases leave, and that by adding a suffi- 
cient number this temperature* could be reduced to that of the 
entering water. Hence, with the counter current principle, tw is 
not limited to the steam temperature and more heat can be 
absorbed by the heating surface than is possible in the ordinary 
arrangement of boiler. Parenthetically it may be remarked that 
without considerable modification the simple arrangement shown 
diagrammatically in Fig. 349 would probably not be satisfactory 
as a boiler element. 

The counter current arrangement is approximated in some 
instances by placing an "economizer" (to be described later) 
beyond the boiler so that the hot gases after leaving the boiler 
surrender some of their heat to the water which passes through 
the economizer on its way to the boiler. So far, the counter 
current principle has been ignored in the design of most boilers, 
but it is approximated in a few types. 

(j) The rapidity with which the gases flow over the heating 
surfaces has a twofold influence on the rate of heat transmission : 
for (i) more heat is conveyed to the surface in a unit of time, 
and (2) the gases are brought more intimately in contact with 
those surfaces, since there is less opportunity for a stagnant 
nonconducting film to adhere to the surfaces. 

(k) The rapid circulation of water within the boiler is of especial 
importance when it is necessary to have high rates of heat 
transmission, for it brings larger amounts of water in contact 
with the heating surfaces in a given time and also prevents the 
metal from becoming overheated. This circulation is brought 
about by providing a free and unrestricted path for the current of 
water and by applying the more intense heat at the proper point 
in this path. In Fig. 350, (a) and {h) show elements of common 
forms of boilers and the arrows indicate the direction of circu- 
lation. The water just above the furnace is less dense than 
that in the other portions of the boiler, since it has absorbed more 
heat and is charged with bubbles of steam, and it therefore rises, 
being replaced by an equal amount of water which descends at 



BOILERS 



543 



points in the boiler where it is colder and denser. This is the 
manner in which the current is established and maintained in 
nearly all the standard types of boilers, as will be seen in study- 
ing the figures in the subsequent sections. 

(1) In some cases this circulation can be made so powerful 
that the water in the ascending column can be discharged at an 




elevation even considerably above that of the surface of the 
body of water from which the descending column receives its 
supply. This can be accomplished with the arrangement shown 
in Fig. 351, in which the arrows indicate the direction of flow. 
The circulation is due to the fact that material in riser A is 
sufficiently charged with vapor to make it weigh less than that 
in the down-comer B, although the altitude 
H is greater than h. As the liberation of 
the steam from the water is supposedly 
more effective when the ascending column 
discharges in this manner, some boilers have 
arrangements somewhat like that shown in 
the diagram. Sometimes a nonreturn valve 
like F is inserted to insure the proper direction 
of flow. After the circulation is once estab- 
lished, however, this valve is no longer neces- 
sary, as the current is then very positive. 

(m) The effectiveness of the heat transmission depends on 
the cleanliness of the heating surface. It is diminished by any 
deposit of soot and dust on the exterior surfaces as well as by any 
interior coating of soft scale (mud) , of hard scale, or of grease. 

Water in its natural state contains more or less foreign matter 
in suspension or in solution. Some of the latter precipitates 
when the temperature reaches about 200° F., still more when 
300° is approached, and the remainder, which is left when the 
water becomes steam, gradually becomes concentrated until it 




544 HEAT-POWER ENGINEERING 

reaches the stage where deposition' occurs. Deposits on the 
water side of the walls of the boiler reduce the heat transmitting 
ability of the plates from o to 20 per cent, depending on the 
thickness of the scale and on the chemical and physical proper- 
ties of the material. 

The formation of scale should be prevented as far as possible 
by purifying the water before feeding it to the boiler; but even 
then there will be some deposit formed which must be removed 
from time to time. Boilers are therefore always so arranged 
that they can be readily cleaned internally, and so that the 
deposit shall, as far as possible, occur at points where the heat is 
the least intense and where the blow-off pipe can be connected 
(as in Fig. 350) so that the softer material can be removed by 
blowing off some of the water from time to time. The exterior 
of the heating surfaces should also be accessible for removing 
the soot and dust. 

262. Boiler Explosions. It has been seen that, by expanding 
steam, heat-energy can be made available which can hz utilized 
in forcing water and steam through the orifice of a nozzle at very 
high velocity. As a result of such discharge there is, of course, 
a force of reaction which will move the nozzle and attached 
parts unless prevented in some manner. The size of this force 
depends, among other things, directly on the area of the orifice. 

A similar process occurs when a boiler shell is ruptured, for, 
in passing through the rent in the boiler shell, the steam and 
boiling water are subject to a decrease from the original pressure 
to atmospheric, and surrender heat which is converted into the 
kinetic energy of the issuing mass. The reactive force acting 
on the boiler shell is dependent in amount on the area of the rent, 
and may be sufficiently great, compared to the weight of the 
boiler, to propel the vessel to a considerable distance. In addi- 
tion to the probable destruction of property and possible en- 
dangerment of lives which may result, the escaping steam and 
water may itself cause considerable damage, — in fact persons 
near by may be seriously, and perhaps fatally, scalded, even 
though the reaction is not sufficient to displace the boiler. 

With boilers containing little water and having elements 
which are of small size and so designed as to have small rents 
when ruptured, the effect of an explosion is less disastrous than 



BOILERS 545 

in the case where a large opening can occur and thus instan- 
taneously release a large mass of water and steam. 

263. Selection of Boilers, (a) There are a great many items 
to be considered in the selection of a boiler for a given service; 
only some of the more important ones can be discussed here. 
Between the various kinds of boilers which have become well 
established there is little choice as regards the efficiency, as their 
performances are substantially equal, hence the selection among 
such standardized types depends largely on general suitability 
for the conditions of operation and space available, on personal 
prejudice and familiarity, on convenience in transportation and 
ease of erection, and on the first cost together with the various 
other items of expense. 

In considering an unfamiliar or untried design the following 
are some of the items to be checked : 

(b) Suitability. It should be decided whether or not the 
boiler is suitable for the coal that is available, and for the kind 
of grates (or stoker) and furnace best adapted to that fuel. In 
special cases where the water is bad and the draft poor these 
items must also be considered. It is not only important that 
the boiler should have sufficient size to meet the normal demands, 
but it should have overload capacity sufficient for all emergencies. 

(c) Safety and Durability. These depend on the design for 
structural strength, on the character of the materials used 
(castings under pressure being avoided) and on the character of 
the workmanship. The arrangement should be such as to avoid 
stresses due to the unequal expansion and contraction of the 
different parts of the boiler; and the method of support should 
be such that the structure, as a whole, is free to adjust itself with 
change of temperature. There should be no thick plates or 
other parts (such as boiler joints) and no projecting portions, 
or plate edges, exposed to the current of the hotter gases; nor 
should the blow-off pipe be exposed to these gases. 

(d) Accessibility. The ability to easily reach all parts of the 
boiler for inspection, cleaning and making repairs, must be in- 
vestigated. Doors in the boiler setting must be provided for 
access to all exterior parts; manholes, or handholes, must be 
so located as to render accessible all internal parts. 

In connection with internal cleaning cognizance must not 



546 HEAT-POWER ENGINEERING 

only be taken of the number of manhole and handhole joints 
to be broken and subsequently made tight, but also of the time 
required for doing this, for cooling the boiler and its setting 
sufficiently to permit of starting such work, and for bringing 
the boiler into commission again. In some water tube boilers 
the dust and soot can be blown from the tubes by means of a 
blast of steam or air issuing from a small pipe which is passed 
through openings in the front and rear of the boiler or its 
setting. Other boilers are provided with openings in the side 
walls for this purpose. 

The design of the boiler should be such as to permit of making 
repairs without difhculty. In most types of boilers the principal 
difhculty is with the tubes. The arrangement should be such 
as to permit readily of the removal and replacement of any one 
of the tubes without disturbing the other tubes or other parts. 
If the tubes are straight but few need be carried in stock, whereas 
if they differ widely in curvature it may be necessary to have on 
hand a large collection to meet any emergency that may arise. 

(e) Circulation of Water. It is necessary to see that the 
arrangement is such as to allow a free and unrestricted circulation 
of the water and that the heat is applied at such a point as to 
establish and maintain the current. The rapidity of circulation 
is of course limited by the smallest cross-section of the circuit. 
The arrangement of the structure should be such that there are no 
pockets where steam can form rapidly and keep the water away 
from the heating surfaces subject to high temperature, for under 
such conditions the boiler shell will burn away at such points. 

(f) Circulation of the Furnace Gases. It is desirable to main- 
tain a uniform velocity of the furnace gases and to avoid sudden 
contraction and expansion as they proceed through the boiler. 
Within limits, the greater the velocity the more rapidly will the 
heat be conveyed to the heating surface and the greater will be 
the amount of evaporation from a given surface. There should 
be no pockets where the gas can remain stagnant and it is de- 
sirable to have the gas bafHed in such a way as to constantly 
bring the fresher portions into contact with the heating surface 
as the gas proceeds. 

(g) Dryness of Steam. To prevent priming, or the entrainment 
of a considerable portion of moisture in the steam, the liberating 
surface of the water from which steam arises should be ample. 



BOILERS 547 

When the water contains certain impurities foaming may occur, 
and this always increases the amount of entrained moisture. By 
providing a large steam space the Hfe of the particles of steam within 
the boiler may be made sufficiently long to allow a more or less 
complete precipitation of the moisture to occur. Provision is often 
made within the boiler for the separation of moisture by means of 
" dry pipes," baffles, or other steam separating devices, 

(h) Quantity of Water. If the boiler contains a large volume of 
water there is less attention required in maintaining the water- 
level, and the boiler has a greater reserve to meet sudden demands, 
than is the case in boilers having a small volume; but greater 
damage would ordinarily result in case of explosion. In marine 
and similar service the greater weight involved is of course 
objectionable. 

(i) Feed Water. The boiler feed should be introduced in such 
manner as not to retard the circulation of the water, and, if cold, 
should not come in contact with the boiler shell. Certain of 
the impurities in solution in the entering water precipitate when 
the higher temperatures are reached and are deposited as mud. 
The water should be introduced at such a point that this precipi- 
tate will be deposited where it will do no damage and from which 
it can be readily removed, see Fig. 350 (a) and (b). Sometimes 
a " mud drum " is provided as in the latter figure, or a " settling 
chamber," as in Figs. 362 and 363, from which the mud may be 
blown off from time to time. 

(j) Space Occupied. In addition to the floor space and height 
occupied by the boiler and furnace, there must be charged against 
the apparatus the amount of space that must be provided for 
the replacement of tubes and for cleaning. In some horizontal 
boilers there must be space in front (or rear) at least equal to the 
length of the tubes (see Fig. 361). This fixes the minimum 
distance between parallel rows of boilers or between the boiler 
end and the wall of the building. In some types of vertical 
boilers sufficient room must be provided overhead for the 
replacement of tubes. 

When the exterior of the heating surface is accessible for 
cleaning from the front or rear of the setting, the boilers may be 
arranged in a continuous " battery " (with adjacent walls in 
common), in which case the walls between boilers are thickened 
slightly. When the cleaning is done from the - side, the boilers 



548 HEAT-POWER ENGINEERING 

are arranged in a series of batteries of two each, with sufficient 
space between the pairs to permit of access to the openings in one 
side of each boiler setting. 

(k) Cost. This, of course, is one of the items of fundamental 
importance. Besides the first cost of the boiler, with its setting 
;and trimmings, and the expense of transportation and erection, 
:it is necessary to consider charges for up-keep and depreciation. 
The size of the boiler and furnace and the space necessary for the 
removal of tubes and for cleaning must also be considered in con- 
nection with their influence on the cost of the ground and building. 

264. Classification of Boilers. Boilers may be classified in 
many different ways, only a few of which need be given here. 

(a) In Internally fired boilers the furnace is located within the 
: structure of the boiler and is usually made integral with it, while in 
externally fired boilers the furnace is placed below the boiler proper 
and is surrounded by a " setting " which is generally of brickwork. 

(b) In fire tube boilers (commonly called " Tubular Boilers ") 
the furnace gases pass through the tubes which are surrounded 
by the water from which the steam is generated; whereas in 
water tube boilers (sometimes called " Tubulous Boilers ") the 
water circulates through the tubes while the hot gases pass over 
their exteriors. Fire tube boilers are shown in Figs. 352 to 359; 
and water tube boilers are illustrated in Figs. 360 to 366. These 
will be discussed later. 

(c) Sectional boilers are composed of small elements so ar- 
ranged that any rupture which may occur will produce only a 
relatively small opening and will result in but little damage to 
the boiler itself and to its surroundings. Such boilers may be 
shipped in small parts which are assembled when being installed. 
Examples of this type of boilers are shown in Figs. 360 and 365. 

(d) In vertical boilers the tubes are arranged perpendicularly, 
or approximately so. In general, such boilers demand less floor 
space than horizontal ones but their height is greater. 

(e) In straight tube boilers it is comparatively easy to clean 
and inspect the tubes. The use of curved tubes is inherent in 
the design of some boilers and they give a certain degree of 
flexibility to the structure. (See Fig. 363.) 

(f) Boilers are also sometimes classed according to their use; 
for example, there are locomotive boilers, marine boilers, portable 



BOILERS 



549 



boilers, stationary boilers, etc. The descriptions which will 
follow, will be limited in most cases to the stationary types. 

(g) There are innumerable arrangements of boilers and their 
settings; only a few of the more typical ones will be considered 
in the following sections. 

265. Internally Fired, Tubular Boilers, (a) Such boilers are 
generally compact and self contained; they are shipped com- 





Fig. 352. — Tubvilar Boiler. 
Submerged Tube Type. 



Fig- 353- — Tubular Boiler. 
Exposed Tube Type. 



plete, and immediately upon arrival are ready to connect to the 
flues and steam system. While they cost more than ordinary 
boilers, they avoid the expense of special brickwork " setting " 
and eliminate the possibility of leakage of air through cracks 
which may develop in such brickwork. Sometimes there is 
difficulty in transporting the larger sizes. 

(b) Fig. 352 shows a small vertical boiler of this kind with 



55° 



HEAT-POWER ENGINEERING 



water level above the tubes. Such boilers are of the submerged 
.tube type. In Fig. 353 is a somewhat similar boiler in which the 
tubes extend above the water level — • the exposed portions pre- 
senting surface to the steam. Boilers of this kind are called ex- 
posed tube boilers. The one shown in this figure is of such large 




Hand Holes 

Fig, 354- — Locomotive Type of Boiler. 



size that the space at a can be occupied by a man while cleaning 
the tubes, the crown sheet and the plates around the furnace. 

(c) Fig. 354 shows a Locomotive type of boiler with a steam 
dome which provides additional steam space. Such boilers are 




Fig- 355. — Continental T)^e of Boiler. 

not only used for locomotives and for traction engines, but also 
for stationary service. 

(d) In Fig. 355 is a longitudinal section of a boiler of the 
Continental type, the exterior of which resembles Fig. 356. 
The furnace wall is a cylindrical flue with strengthening cor- 



BOILERS 



551 



rugations. The combustion chamber is lined with fire brick or 
other refractory material and is located in a casing of thin metal 
extending from the main shell of the boiler. These boilers have 
large liberating surface, voluminous steam space and large 
volume of water. They usually have either one or two furnace 
flues, and because they are compact and have short tubes, they 
can be used in places where the space is limited. 

(e) The Scotch Marine type of boiler is shown in Fig. 356 and 
is similar to the Continental except that its combustion chamber 



Uptake 




356. —Scotch Marine Type of Boiler. 



(see Fig. 357) has metal walls and is entirely surrounded by 
water. As these walls tend to collapse under the external 
pressure to which they are subjected, they are carefully stayed. 
Such boilers have from one to four corrugated furnace flues, and 
their outer shells range from 5I feet to 16 feet in diameter. Be- 
cause of the very short tubes, large steaming capacity for space 
occupied, absence of brick setting, and accessibility, they are 
particularly adapted to marine service. 



266. Externally Fired Tubular Boilers, (a) Boilers of this 
type generally require a separately constructed " setting " 
(usually of brickwork with lining of firebrick) to surround the 



552 



HEAT-POWER ENGINEERING 



furnace and boiler. This is so arranged as to properly confine 
the flue gases and guide them to and from the boiler. It takes 
considerable time to construct and dry out the brickwork setting 




Fig- 357- — Submerged Combustion Chamber. 



and the expense involved must be added to the cost of the boiler 
itself. Such boilers usually occupy more space than internally 
fired boilers and the setting should be kept in repair so as to 




avoid air leakages, which have a detrimental effect on the draft 
and boiler performance. 

(b) An externally fired boiler classified as of Horizontal Return 
Tubular type {" H.R.T. boiler ") is shown in Fig. 358. In this 



BOILERS 



SS^ 



boiler the smoke box is formed in an extension of the boiler 
shell which projects beyond the brick front wall. The cast iron 
" boiler front " covers only the portion of this wall located 
below the smoke box, and is therefore commonly called a " half- 
front." The boiler shown in this figure is suspended from cross 
beams or " Gallows frames." 

(c) In Fig. 359 is shown a H.R.T. boiler with "full flush 
front,'' the smoke chamber being formed in the brickwork of 
the front wall. The boiler is shown to be supported by brackets, 




Fig- 359- 



3uck stave 

•Horizontal Return Tubular Boiler with " Full Flush Front." 



the rear pair of which is mounted on rollers to allow free ex- 
pansion. The brick setting is braced by " buck staves." 

As most of the scale is deposited at the rear of the boiler, as 
in Fig. 350 (a), the blow off is located at this point. The back 
end of the boiler is lowered slightly to aid in draining the shell. 

As the boiler shell is exposed to the direct heat of the furnace, 
the thickness of metal must not be so great as to make it liable 
to burn thinner, and as the shell thickness must increase with 
the diameter of the boiler, these boilers cannot be constructed 
beyond a certain size. They are not ordinarily built larger than 
200 boiler horse power and are seldom used with pressures above 
150 pounds. The H.R.T. boilers are about the cheapest made, 
hence are quite widely used for low pressures. 



554 



HEAT-POWER ENGINEERING 



267. Water Tube Boilers, (a) Figs. 360 and 361 illustrate 
sectional water tube boilers known as the Babcock and Wilcox 
type (or " B. and W." type). The tubes are expanded into 
pressed steel front and rear " headers " to form tube " sections." 
The sections, the drums, connecting nipples and other parts are 
shipped " knocked down," and are assembled at the power house. 
The parts to be transported and handled are therefore relatively 
small. Being of the sectional type with small elements, the 
danger of disastrous explosions is slight, as ruptures seldom occur 




Fig. 360. —B. and W. Type of Boiler. 



elsewhere than in the tubes. Opposite each tube is a hand-hole 
cover which can be removed for cleaning and replacing tubes. 
Doors for external cleaning are provided in the side walls, hence 
these boilers cannot be arranged in continuous batteries, but 
they may be grouped in batteries of two each. The boiler has 
elements similar to {h) in Fig. 350, with mud drum located at the 
bottom of the rear headers. It is hung from above, hence is 
free to expand or contract. 

As shown in the figure the furnace has an exposed roof and the 
gases are baffled so as to make three " passes " across the tubes. 



BOILERS 



555 



Other arrangements of bajffles and furnace can of course be used. 
The tubes are not arranged in vertical rows, but are " staggered," 



-^i. 







Fig. 361 — B and W, Tj^ie of Boiler 



as shown by the header at (a) in, Fig. 360, so as to further baffle 
the gases. 

(b) In Fig. 362 is shown the Heine type of water tube boiler 
having the front and rear " water legs " made of steel plates and 




Fig. 362. — Heine Type of Boiler. 

riveted to the drum. The front and back plates of each water 
leg are held together by hollow stay bolts having holes' large 
enough to permit the insertion of a steam or air pipe for blow- 
ing the soot and dust from the exterior of the tubes ; and opposite 



556 



HEAT-POWER ENGINEERING 



Precipitati 
Pocket 



each tube in each water leg is a hand hole giving access to the 
interior of tubes. 

The feed water enters a " mud drum," where it remains 
quiescent for a considerable time before it mixes with the water 
which is circulating through the tubes. As this feed water be- 
comes heated certain of the impurities are precipitated in the 
mud drum, from which they can be blown off at intervals. 

The water legs of the boiler shown in the figure rest on the 
brickwork and have rollers under the rear one. The boiler may, of 

course, be supported 
in other ways. This 
boiler is shipped com- 
pletely assembled, 
ready to have the set- 
ting constructed im- 
mediately upon its 
arrival. As no clean- 
ing doors are located 
in the side walls, such 
boilers can be arranged 
in continuous batter- 
ies. 

As shown, the fur- 
nace has a tile roof 
supported by the lower 
row of tubes and the 
furnace gases are baf- 
fled so as to pass along 
the tubes. The same type of boiler is often used with baffles 
arranged similar to those in Fig. 361. 

(c) Fig. 363 shows the Stirling type of water tube boiler which 
may be classed as a vertical one. It is composed of drums and 
tubes which are not assembled until they reach their destination. 
Since the elements are simple and easy to make, the cost of such 
boilers is less than that of those having more complicated parts. 
The feed water enters a precipitation pocket in drum D and is 
heated as it descends to drum C. The circulation of water is 
through tubes joining drums A, B and C. All the upper drums 
are connected by steam pipes. 

The rows of tubes running circumferentially around the drums 




Fig. 363. — Stirling Type of Boiler. 



BOILERS 



557 



are arranged in pairs, between which is sufficient space for the 
removal or insertion of tubes located in the interior of the nests. 
The tubes are curved and the mud drum is suspended by the 
tubes — an arrangement which gives flexibility and permits of 
expansion and contraction accompanying temperature changes. 
All drums have man holes which give access to their interiors 
and to the tubes. The side walls of the setting are provided 
with cleaning doors exposing the exteriors of the tubes, hence 




Fig. 364. — Wickes Type of Boiler. 

these boilers cannot be arranged in continuous batteries — 
they may, however, be arranged in pairs. The arrangement 
provides for large combustion space and for an ample coking 
arch, or Dutch oven roof. 

(d) There are many other arrangements of boilers composed 
of simple horizontal drums and vertical tubes. In some the 
vertical tubes enter a single upper drum and a single lower one, 
and the gases are bafifled so as to make two or three passes. 

In other boilers there are two drums above, with steam and 
water connections between, and two lower drums, with water 



558 



HEAT-POWER ENGINEERING 



connections, and between these pairs are vertical tubes. The 
furnace gases pass up along the tubes joining the front drums 
and down along the rear tubes, to a flue connection near the bot- 
tom of the setting. There are still other arrangements, but those 
given will suffice to show the possibilities of this construction. 

(e) Fig. 364 shows the Wickes type of vertical water tube 
boiler having single upper and lower drums with vertical axes. 
The tubes are removed and inserted through hand holes located 
in the dome of the steam space; hence, it is necessary to provide 
overhead room, or sky-lights, immediately over the boilers. 




Fig. 365. — Parker Type of Boiler. 



(f) In Fig. 365 is shown the Parker type of boiler, which dififers 
radically in several respects from the ordinary types, since it 
makes use of the counter-flow principle (Sect. 261 {i)) and de- 
livers the steam and water at points above the water level 
(Sect. 261 (/)). Under the best conditions of operation, the 
feed water enters the system at A (check valve E being closed), 
passes downward through the zig-zag tubes in a general direction 
opposite to that of the ascending flue gases (just as in Fig. 349) 
and is finally delivered at B into the drum, with a temperature 
high enough to cause the precipitation of most of the impurities. 
The water from the drum enters another set of zig-zag pipes at 
C, constituting the vaporizing element, is further heated as it 
descends and is finally discharged as steam into the drum at D. 



BOILERS 559 

Owing to the countercurrent flow it is possible, by providing 
sufficient heating surface, to cool the flue gases below the temper- 
ature of the steam. Hence, sometimes a third nest of tubes is 
added, in which case the upper is called an " economizer element." 

Should the feed valve be shut off the circulation will still con- 
tinue, for water will then pass through check valve E into the 
upper element of tubes, but the operation will be somewhat less 
efficient than before. 

The " junction boxes " joining the ends of the tubes have 
hand holes and some have non-return valves which ensure the 
circulation of the water in the proper direction. Besides the 
scale pocket F there is a blow off (not shown) located under the 
diaphragm in the bottom of the drum. 

(g) In boilers of the porcupine type, the tubes, with closed 
outer ends, project from a water drum, or header, Into the path 
of the flue gases. Fig. 366 shows an arrangement having a 
double header and concentric tubes. With such arrangement the 
cold water descends through the left water leg, passes through 
the inner tube to the end, then returns through the annular 
passage between the two tubes and ascends in the riser to the 
steam drum above. But little use is made of this arrangement, 
however, because of the expense of construction. 



tit t 




H 



'Flue Gas I ] ]" 



Fig. 366. — Niclausse Tubes. 



(h) Fig. 367 shows a double-furnace boiler arranged to be fired 
from both front and " rear "; thus it has about double the grate 
area and generates steam nearly twice as rapidly as in the ordi- 
nary case. However, as the rate of evaporation is high the 
efficiency is slightly less than is obtained under less intensive 
conditions. Such arrangements are frequently adopted when 
floor space is limited or when the cost of real estate is great, as 
is the case in power plants located in congested districts of large 
cities. The same scheme can, of course, be used with boilers of 
other types than that shown. 



56o 



HEAT-POWER ENGINEERING 



268. Boiler Accessories. In addition to the fittings already 
described, boilers are always fitted with steam gauges, glass 
water gauges, try cocks, safety valves, feed valves, blow-off 
valves and steam stop valves. In addition they frequently have 
" water columns " with floats to operate sentinel whistles when 




Fig. 367. — Double-furnace Boiler. 



the water level becomes too high or too low ; and they may have 
" fusible plugs " which, when the water level becomes danger- 
ously low, become uncovered and melt, and thus allow steam to 
escape and attract attention before the plates become over- 
heated. Automatic feed-water regulators are sometimes used, 
and in plants where the load fluctuates rapidly damper regula- 



BOILERS 561 

tors, controlled by the steam pressure, are also provided to 
automatically adjust the draft. When water tube boilers are 
used, the boiler room equipment generally includes mechanical 
tube cleaners, of which there are many varieties. 

269. Boiler Performance, (a) In stating the evaporative 
performance of boilers and similar apparatus, it is customary to 
use the latent heat of vaporization of one pound of steam at 
atmospheric pressure as the " Unit of Evaporation " (U.E.). 
The value of this unit is, therefore, 970.4 B.t.u. (old value 965.7) ; 
and, as this is the heat absorbed by one pound of steam in being 
converted from water with temperature of 212° F., to steam at 
the same temperature, the performance may also be stated in 
terms of the " Equivalent Evaporation " or " number of pounds 
of water from and at 212° F." that would be evaporated by the 
same amount of heat. Evidently there would always be the 
same number of pounds of Equivalent Evaporation as there are 
Units of Evaporation. 

When boilers are tested, the temperature of the feed water, the 
actual weight of steam generated per hour, and the quality (or 
superheat) are all determined. With these quantities known, the 
equivalent evaporation from and at 212° F. can be determined by 
dividing the heat given to water and steam by 970.4 (965.7). 

(b) This same unit can also be used for expressing the value 
of fuels when used for generating steam; thus, the Theoretical 
Equivalent Evaporation (T.U.E.) per pound of fuel is found by 
dividing the calorific value per pound by 970.4. 

Based on the usual calorific values, the T.U.E. 's per pound of 
combustible, are about as follows for the different kinds of fuel : — 
Carbon, 15 pounds; good anthracite, 15.4 pounds; semi-bitumi- 
nous, 16.3 pounds; bituminous, 14 to 15.8 pounds; and oils, 
18.5 to 22 pounds. 

Obviously the Theoretical Equivalent Evaporation per pound 
of fuel can be obtained by multiplying the foregoing figures by 
the percentage of combustible present. 

(c) The steam generating apparatus as a whole delivers with 
the steam only a portion of the calorific value of the fuel, the 
percentage depending on the overall efficiency of the apparatus. 
These efficiencies were given in Sect. 260 {h) and {i). With 
good coal the Actual Equivalent Evaporation should be at least 



562 HEAT-POWER ENGINEERING 

9 pounds per pound of combustible, and in the best instances 
I2| pounds have been reached. With oil this evaporation is 
from 14.4 to 16.9 per pound of fuel. 

When the rate of evaporation is under consideration, the unit 
of time generally adopted is the hour — hence the terms "Equiv- 
alent Evaporation per hour " and " Units of Evaporation per 
hour " are in common use. If no unit of time is specified the 
hour is implied. 

(d) In boiler computations it is sometimes convenient to make 
use of a quantity called the " Factor of Evaporation " (F.E.). 
This quantity is the ratio of the heat absorbed per pound of 
steam generated to 970.4 (or 965.7 as the case may be). Hence 

Factor of Evaporation = — /^ — '—z ^ ^-^. . (406) 

970 (or 965.7) '^ 

in which q, x, r, D and Cp are respectively the sensible heat, 
quality, latent heat, degrees of superheat and specific heat 
of the steam leaving the boiler, and / is the temperature of the 
feed water. Evidently the Factor of Evaporation is the ratio 
of the actual weight to the equivalent evaporation, and as this 
ratio is frequently used its values are generally tabulated in 
reference books for different pressures of dry saturated steam 
with various temperatures of feed water. 

(e) The rated size and the maximum capacity of boilers are 
usually stated in terms of a unit miscalled a "Boiler Horse 
Power" (B.P.). It has been suggested that this be changed 
to " Boiler Power,'' as the term " horse power " is inapplicable 
to boilers. The Boiler Horse Power is defined as the equivalent 
of 34-5 pounds of steam evaporated " from and at " 212° F. 
per hour; (i.e., 34I U.E. per hr.). It is, therefore, merely a 
measure of the heat given to the water and steam and is equiva- 
lent to the transfer of 33,479 B.t.u. per hour (with U.E. = 970.4 
B.t.u.). 

The " horse power " of a boiler which is evaporating a given 
weight of steam per hour at a certain pressure, with a certain 
quality, and from feed water at a certain temperature, can there- 
fore be found in two ways: — First, by dividing the equivalent 
evaporation by 34I; second, by dividing the total heat supplied 

* The expression in this parenthesis is written so as to apply to both super- 
heated and saturated steam, as was first done on page 173. 



BOILERS 563 

to the water and steam per hour by the number 33,479 given 
above. 

(f) In this connection, however, it is important to note that 
there is no definite relation between engine horse power and the 
so-called boiler horse power; the ratio of the engine h.p. to the 
" boiler h.p." in any plant depends entirely upon the economic 
performance of the engine, hence it is not necessarily the same in 
different plants. 

270. Proportioning the Boiler for Power Output, (a) The 

American Society of Mechanical Engineers has made the follow- 
ing recommendation regarding boiler ratings. " A boiler rated 
at any stated capacity should develop that capacity when using 
the best coal ordinarily sold in the market where the boiler is 
located, when fired by an ordinary fireman, without forcing the 
fires, while exhibiting good economy. And further, the boiler 
should develop at least one-third more than the stated capacity 
when using the same fuel and operated by the same fireman, 
the full draft being employed and the fires being crowded, the 
available draft at damper, unless otherwise understood, being 
not less than one-half inch water column."* Boilers of the 
commercial ypes generally have overload capacity considerably 
in excess of the 33^ per cent here specified. Some boilers are 
being operated continuously under loads double those for which 
they were originally intended, and triple outputs have been 
obtained in a few instances. 

(b) The total amount of heating surface needed by boilers 
can be determined either by multiplying the boiler " horse 
power " by the number of square feet needed for developing 
one horse power, or by dividing the total equivalent evaporation 
per hour by the allowable rate of evaporation per square foot. 

(c) Most stationary boilers of the " water tube " type have 
10 square feet of heating surface per boiler horse power under 
normal load, the corresponding rate of equivalent evaporation 
per square foot per hour being about 3I (= 34.5 -J- 10); while 
the more common types of stationary " fire tube " boilers usually 
have 12 or more square feet per boiler horse power, the equivalent 
evaporation being 3 pounds per square foot or less. However 
values both larger and smaller than these are sometimes used. 

* Trans. A. S. M. E. 1899. 



564 HEAT-POWER ENGINEERING 

When there are Hmitations as to space or weight, less heating 
surface and higher rates of evaporation are used. For example, 
in marine boilers from 4 to 8 square feet of heating surface are 
provided, the corresponding evaporation being from 8 to 4 
pounds per square foot per hour, and in some instances marine 
boilers of the water tube type have been operated continuously 
with average rates as high as 16 pounds.* 

(d) The fuel needed per boiler horse power hour can be 
readily determined by dividing 34I by the equivalent evapora- 
tion per pound — or by dividing 33,476 by the actual calorific 
value per pound. Thus the combustible required per boiler 
horse power ordinarily ranges from 3 to 4 pounds per hour, de- 
pending on the kind of coal, and the weight of coal is roughly 
from 3.5 to 5 pounds. 



Melville, Engineering Magazine, January, 191 2. 



CHAPTER XXXI. 

SUPERHEATERS. 

271. Advantages of Superheating, (a) It has aheady been 
shown (Sect. 128 and i8oj) that the water rates of steam engines 
and turbines may be materially improved by the use of super- 
heat, but that the improvement in steam consumption is not a 
correct measure of the gain effected, since one pound of super- 
heated steam contains more heat than an equal weight of satu- 
rated steam at the same pressure. Leaving out o-f consideration, 
for the time being, certain incidental advantages of superheating, 
the true measure of gain is on the basis of the keat economy 
resulting from its use and this is given by the ratio of the number 
of heat units supplied to the superheated steam, per horse power 
delivered by the engine or other prime mover, to that used when 
saturated steam is the v/orking substance. 

(b) In addition to such gains as may be efifected in the prime 
movers themselves by the use of superheat, there may be a two- 
fold reduction in the heat lost in the connecting pipe lines, be- 
cause (i) superheated steam loses heat much less rapidly than 
does wet steam and because (2) the radiating surfaces of the 
pipes may be made less — for smaller pipes can be used, as super- 
heated steam may be allowed to flow at higher velocities than 
are permissible with saturated vapor. 

(c) But the ultimate test of the advisability of installing 
additional apparatus, such as superheaters, is always on the 
basis of the financial economy efifected. In the case in question 
the addition of the superheaters may not increase the total 
expense for the power plant equipment, for the improvement 
in heat economy may permit a reduction in the size and cost of 
the boilers, and the diminution of the water rates may make 
possible a decrease in the size and cost of the condensers and 
other auxiliary apparatus. Then, the operating expenses may 
be reduced not only by the saving in the expenditure for fuel but 
also by the reduction in the outlay for purchasing and pumping 

565 



566 HEAT-POWER ENGINEERING 

the water used for feed and for condensation. To offset the gains 
is the additional expense involved in the operation and mainte- 
nance of the superheaters. The use of the smaller pipe lines, which 
are permissible with superheated steam, may not effect a saving 
in their cost, as the materials, construction and fittings must be 
of better quality than is required when saturated steam is used. 

272. Types of Superheaters, (a) There are two general 
types of superheaters — (i) separately fired superheaters, and 
(2) built in, or boiler draft superheaters. 

The first class is installed in a separate setting of its own and 
receives hot gases from its own furnace. The second class is 
located inside of the boiler setting and in line with one of the 
" passes " of the products of combustion. 

(b) In each type the saturated steam,' generally containing 
from 2 to 4 per cent of moisture, is led from the steam nozzle on 
the drum of the boiler, through the superheating apparatus on 
its way to the steam consumer. 

(c) Superheaters of both types generally consist of a multi- 
plicity of elements containing a small volume but exposing a 
relatively great surface. There are, however, several super- 
heaters in which a few very large elements are so constructed 
that, by means of baffles or equivalents, the steam flowing 
through them is divided up into thin streams in contact with 
extended wall areas. 

(d) Generally the metal used is mild steel, and the elements 
are composed of seamless tubes which are of small diameter 
(i inch to i| inch bore) with thick walls (0.15 to 0.2 inch 
thick) and which are connected with built-up, forged, or cast steel 
headers or their equivalents. In a few instances cast-iron ele- 
ments with comparatively thick 
walls are still used, but there is 
a growing tendency to look with 
suspicion on the use of this ma- 
terial in cases where temperatures 
and pressures are high and where 

Fig. 368. temperature changes are great. 

Figs. 368 and 369 show the two 
elements most commonly used in this country. Instead of hav- 
ing the tube ends enter separate headers, they are sometimes 




SUPERHEATERS 567 

connected with a single one arranged with suitable partition 
plates or baffles. The element shown in Fig. 369 has a thin 
annular steam passage between a sealed inner tube and an outer 
one which is surrounded by flanges. The flanges, which are of 
cast iron, present large heat-absorbing surfaces to the hot gas, 
protect the steel tubes and store heat, but add to the expense of 
construction. The steam is brought intimately into contact with 
the walls of the larger tube, since it can flow through the thin 
annular passage only. 

(e) Experience has shown that the ideals to be attained in 
superheater construction and arrangement are: (i) perfect free- 
dom of expansion; (2) ability to withstand high temperature, 
high pressure, and violent changes in temperature; (3) avoid- 



Fig. 369. 

ance of screwed joints; (4) the protection of all joints from ex- 
posure to the hot gases; (5) provision for cleaning externally 
and internally; (6) means for adjusting the superheat to any 
desired temperature; (7) natural, or automatic, regulation to 
maintain that temperature; (8) means of bypassing the steam 
around the superheater when the latter is out of commission; 
(9) provision for flooding the elements (in some cases) with water 
and for draining them; (10) small space requirements; (ii) low 
first cost; and (12) small expense of operation and maintenance. 

273. Separately Fired Superheaters, (a) Two examples of 
separately fired superheaters are illustrated in Figs. 370 and 371. 
In all such apparatus it is nearly always necessary to prevent the 
flame and very hot gases from impinging directly on the super- 
heating surface, it being generally considered that temperatures 
of from 1300 to 1500° are the highest allowable for the gases 
which are in contact with such surfaces; hence, the use of inter- 
cepting brick arches and walls through which the hot gases must 



568 



HEAT-POWER ENGINEERING 



pass, as shown in Fig. 370, though a greater degree of security 
is attained by combining a water element with these walls, as 
shown in Fig. 371. 

(b) The temperature of superheat may be controlled directly 
by varying the rate of combustion, by means of a damper, as in 
Fig. 371 ; by bypassing the gases, or by both of these methods, 
as in Fig. 370. But even if the dampers be made to normally 
follow the delivery temperature exactly, as can be done by 
means of thermostatic control, the heat stored in the walls of 
the setting will cause an abnormal rise of temperature when the 




Fig. 370. 



demand for steam suddenly decreases to any considerable extent. 
Then there may also be sudden drops in the temperature due 
to the inflow of cold air when the furnace doors are opened for 
firing. 

(c) Compared with the built-in type, the separately fired 
superheater has many disadvantages, of which the principal ones 
are: (i) Greater first cost because of the separate setting and 
grate; (2) larger maintenance cost because of separate setting; 
(3) greater cost of operation because of separate furnace to be 
fired; (4) greater floor space occupied; (5) grate losses, which 
in this case are added to those of the boiler; (6) lower efficiency 
because the flue gas enters the stack at a temperature which 
must be higher than with built-in type, where superheater is 
followed by water heating surface; (7) greater radiation loss 



SUrii.RHEAThP.S 



569 



because of individual setting; and (8) difficulty of controlling 
temperature of steam, as explained in (b) above. The separately 
fired superheater has the advantage that the boilers can still be 
used to supply saturated steam even when the superheater is out 
of commission; that it permits the variation in the degree of 
superheat to be made independently of the operation of the 
boiler, and one superheater can be used for several boilers. 

(d) Although it has many disadvantages, the separately 
fired apparatus may be of value in many instances. In some 
plants, steel mills for instance, there are often large quantities 
of hot gases which, by such apparatus, can be used to superheat 
the steam coming from the boilers, but which would otherwise 




Fig. 371. 

be wasted. Then, there are also many industries in which steam 
exhausted from engines is used in some manufacturing process, 
and in many such cases it is desirable to superheat this steam in 
separately fired superheaters. Again, either as a means of im- 
proving the economy or of increasing the capacity of a boiler 
plant already installed, it may be desirable to superheat the 
steam generated, and in such cases it will generally appear upon 
investigation that the separately fired unit is the better invest- 
ment, as it will involve least changes in piping and settings. 



274. Boiler Draft Superheaters, (a) Examples of this type 
are illustrated in Figs. 372 to 374. In nearly all cases 
built-in superheaters are installed at such a point in the flues, or 
gas passes, that the temperature of the gas reaching them can 
never greatly exceed about 1500° F. There are a few instances, 



570 



HEAT-POWER ENGINEERING 



however, as in Fig. 372, in which the superheaters are installed 
in a separate brick chamber within the boiler setting and are 
supplied with hot gases directly from the furnace, by means of a 

passage in the brick walls 
of the boiler setting, the 
flow of gas being controlled 
by a damper in the passage, 
(b) Two distinctly dif- 
ferent methods of main- 
taining an approximately 
constant temperature of 
superheat are in use. In 
one, the superheating ele- 
ments are located at such 
a point (as in Fig. 373) that 
the gases reaching them 
vary in temperature and quantity as nearly as possible in propor- 
tion to the amount of steam flowing. The attainment of such 
conditions is generally more ideal than real, but is fairly well 
approximated in a few instances, since the amount of steam gen- 




Fig. 372. 




from Furnaces 



elated depends directly on the quantity and temperature of the 
gases coming from the furnace. 

In the other method the superheating elements are installed 
within a separate chamber, as in Figs. 372 and 374, and a damper, 
which regulates the supply of hot gases, is put under some sort 
of control, which may be thermostatic. These superheaters 
have a certain temperature lag, as do the separately fired variety, 



SUPERHEATERS 



571 



iDut it is not as great as in that case because of the smaller amount 
of brickwork surrounding them. 



275. Protection of Superheater, (a) No superheater, no 
matter what its construction, will last for any considerable 
length of time if exposed to the hot furnace gases when steam 
is not flowing through it. To prevent damage in this way, 
during the period of firing up and when cooling down or standing 
idle, some protective device is essential. 

• (b) With separately fired superheaters the hot gases may be 
deflected, as in Figs. 370, 372, and 374, so that they bypass the 
superheater and flow directly from the 
furnace to the stack, or protecting rings 
like those in Fig. 369 may be used, or 
provision may be made for " flooding " 
the superheater — that is, filling it with 
water whenever the flow of steam 
ceases. The latter method is open 
to the objection that scale-forming 
material may be deposited in the 
superheater, thus decreasing its ability 
to transfer heat from gases to steam, 
which would ultimately result in main- 
taining the metal of the superheater at 
too high a temperature when in opera- 
tion and thereby shortening its life. 

(c) When boiler draft superheaters 
are located in a separate chamber within the boiler setting, either 
of the above methods may be used, but the objection to the last 
holds equally well for this case. 

(d) When boiler draft superheaters are located directly in one 
of the passes the only available method of protecting is by flood- 
ing. They are generally so arranged (as in Fig. 373) that when 
flooded they form part of the boiler evaporating or heating sur- 
face, practically being connected in parallel with it, but so that 
they can be drained and connected in series with the boiler when 
superheat is desired. 

(e) In connection with this latter arrangement, an auxiliary 
safety valve is sometimes placed between the superheater and 
the main stop valve, so that if this latter valve is suddenly closed, 




Fig. 374- 



572 HEAT-POWER ENGINEERING 

or if the demand for steam suddenly ceases, before the fires cart 
be deadened, the rising pressure of steam will pop this safety 
valve (before the main safety valve opens), and allow steam ta 
pass through the superheater, thus protecting it temporarily 
and warning the attendant of the necessity for checking the fire 
and, possibly, for flooding the apparatus. 

276. Superheater Surface, (a) The determination of the 
amount of surface required by a superheater to give a definite 
degree of superheat, when fired in a certain way, or located in a 
given position, is largely a matter of experience with each manu- 
facturer of each different type of boiler. There are several 
distinct methods of approximating the amount of super-heating 
surface required; the three most common are given below. 

(b) The superheating surface may be taken as a multiple of 
the grate surface. Thus for water tube boilers, the heating sur- 
face of built-in superheaters is generally taken at from 8 to 12 
times the grate area, depending upon location within the setting,, 
average rate of firing, superheat desired, character of coal, etc. 
With long flaming coals the gases often arrive at the superheater 
at a higher temperature than with short flaming fuels and a 
smaller surface may therefore be used. 

For internally fired boilers, values between 25 and 35 times 
the grate area are used. 

(c) The superheating surface may be taken as a fraction of the 
boiler heating surface. For water tube boilers it varies between 
10 and 40 per cent of the boiler heating surface, though it rarely 
exceeds 20 to 30 per cent. For internally fired boilers a greater 
ratio is required, reaching in some cases to values almost equal to 
the boiler heating surface, and seldom dropping below 50 per 
cent of that surface. 

(d) The number of square feet of superheating surface (S) 
required may be determined by calculations, taking account of 
rate of heat transmission per square foot per hour, which depends 
both on the coefficient (K) of heat transmission and mean 
temperature difl^erence (9m) between steam and gases. In this 
case, the heating surface required to transmit per hour an amount 
of heat equal to AQ is 

^=l£-' (407) 



5 UPERHEA TERS 573 

The coefficient {K) is the heat (B.t.u.) transmitted per square 
foot of surface, per degree difference of temperature, per hour. 
Its value varies widely with conditions and is found by experi- 
ment or experience. High velocity, thin streams of steam or 
gas, violent agitation, and high temperature and pressure, in- 
crease its value. The condition of the superheater also has 
considerable effect; when scaled internally and covered with 
ash and soot externally, the rate of transmission is very low. 

In general, values of K vary from i to as high as 10, and con- 
siderable experience is required in choosing a proper value. 



CHAPTER XXXII. 
DRAFT AND DRAFT APPARATUS. 

277. General Principles, (a) The flow of air and products 
of combustion through the steam-generating apparatus is re- 
tarded by the resistances encountered in the various portions of 
the passage. The total resistance (R), from the point where the 
air enters the boiler setting to the base of the stack, is the sum- 
mation of the resistances of the fuel bed (Rf) , of the boiler passages 
(Rp) , of the flues or breeching (Rb) and of any other passages (R^) 
(such as that through an "economizer") which are traversed. 
Thusi? = Rf -{- Rp -i- Rb -i- Rx. It is of course desirable to have 
the total resistance as small as possible, hence each component 
resistance should be reduced to the fullest extent allowable. 

(b) As the gases flow only from places of higher pressure to 
those of lower (through a process of expansion) the gas pressures 
must decrease progressively from the point of entrance to the 
point of exit, the pressure drops through the different portions 
depending on the respective resistances of the parts. 

The way in which the pressure varies, as the particles of gas 
advance through the steam-generating apparatus, is shown in a 
general way in Fig. 375 by the curve abed, in which the abscissas 
represent the decrease of pressure below that at the point of 
admission and the ordinates are distances along the passage, 
measured from the same point. 

Evidently, the same curve would apply (in this particular 
case) regardless of whether the inlet pressure is atmospheric, or 
greater or less than that, for the same pressure drops and the 
same gradients to the curve would still be required. The differ- 
ence between the abscissas of any two points on this curve gives 
the pressure drop required to overcome the resistance between 
the corresponding points in the apparatus. The final abscissa 
represents the pressure drop developed through the whole ap- 
paratus, and is evidently equal to the summation of all the 
pressure drops, i.e., AP=AP/ -f APp -{- APb + APx, in which 

574 



DRAFT AND DRAFT APPARATUS 



SIS 



the subscripts refer to the same parts as before. It is the func- 
tion of the stack, or other draft-producing device, to develop this 
difference in pressure. 

(c) As the pressure variations of the flue gas, measured from 
atmospheric pressure, are very low, they are ordinarily deter- 
mined by means of water manom- 
eters, as shown in Fig. 375, and are 
therefore commonly expressed in 
terms of inches of water column 
(" hydraulic inches ") as compared 
with atmospheric pressure.* 

The total pressure drop from air 
inlet to base of stack is generally 
between 0.4 and i .2 inches of water 
when determined in this way. 

The velocity of flow is generally 
so small that the velocity head can ^a&ap 
be neglected in the ordinary prob- 
lems that arise in connection with Fig. 375. 
the subject under discussion. 

(d) According to Bernoulli's theorem (which can be applied to 
the steady and continuous flow of gases in long pipes when there 
are small pressure drops), the total head is the same at all points 
in the passage. At the point (o) of entrance it is the sum of the 

velocity head ( — j , the pressure head (t) > ^"^i ^^^ potential 
head Zq; and at any subsequent point {x) it is the sum of the 
similar heads for that point together with friction head F of the 
intervening passage. Thus 




ify^-i<h-'.-i 



+ F, 



(408) 



'0 \zg 8 
in which v = velocity of flow in feet per second, 
P = pressure In pounds per square foot, 
8 = specific density = weight per cubic foot of gas, and 
2 = elevation in feet. 
The friction head (ft.) is 

F = f—LX^ (409) 



2g A' 



* One inch of water column corresponds to 
or one pound per square foot corresponds to .19 



62.5 



= 5.2 pounds per square foot; 
inches of water column. 



576 HEAT-POWEk ENGINEERING 

in which L = length of flue in feet, 
/ — coefficient of friction, 

S = length of perimeter of the cross-section in feet, 
A = area of passage in square feet, 

and the ratio A/S is called the " mean hydraulic radius." 

In the passages through the boiler the variation in velocity and 

in elevation can ordinarily be neglected, hence the quantities v 

and z disappear from Eq. (408) in this case. 

Then from Eqs. (408) and (409), using a mean density 5^ and 

letting AP = (Pq — Px), the change in pressure head is 

-K^^=^7g^A' (410) 

which shows that the pressure drop is dependent solely on the 
frictional resistance, which varies directly with v^, L and the 
character of the surfaces and inversely with the mean hydraulic 
radius (A/S). 

The velocity of flow is, from Eq. (410), 



v=V2gAPX{A^fLS8m). . . . (411) 
and for any given passage 

V = const VAP (412) 

Evidently the rate of combustion, which is dependent on the 
velocity (amount) of the air passing through the fuel bed, can be 
reduced by decreasing A in Eq. (411), other things remaining 
the same, as by partly closing the damper. 

(e) But in the actual case of flow of gases through steam-gen- 
erating apparatus, the conditions are quite different from the 
hypothetical ones assumed in connection with Bernoulli's The- 
orem, — for, through part of the passage there is air of a certain 
density, through the rest is a complicated mixture of gases 
varying as to composition, density and temperature; the passages 
are circuitous, have sudden changes in areas and in direction 
and have eddy pockets; the resistance through the fuel bed is 
constantly varying and the flow of gas is neither steady nor 
necessarily continuous, — hence, the analysis of the laws gov- 
erning the actual case is difficult and as yet these laws are not 
well established. 

There are, however, a few general statements which can be 
made and which are more or less applicable to most cases ; they 



DRAFT AND DRAFT APPARATUS 577 

may serve as rough guides in approximating the solution of 
problems connected with boiler draft.* These are given in the 
following paragraphs. 

(f) Other conditions remaining the same (temperatures, re- 
sistances, etc.), the weight (w) of air entering the furnace in a 
unit of time is dependent on the velocity of flow, and appears 
to vary about as the square root of the pressure drop (AP) 
through the passages. f As the rate of combustion (R) is directly 
dependent on the air supply it varies approximately in like man- 
ner, i.e., R = const. VAP, where the constant varies with the 
size and kind of coal, method of firing and other conditions. 
Thus, doubling the pressure drop increases the rate to about 
1.4 (= V2) its former value; and to burn fuel twice as rapidly 
as before involves nearly quadrupling the draft pressure. 

(g) It is also approximately true that if the resistances remain 
unchanged, the pressure drop through any portion of the passage 
will remain the same fraction of the total, regardless of the vari- 
ation in the over-all drop, that is, the pressure gradients would 
vary proportionally. For example, for the case shown in 
Fig. 375, with change in draft, the curve would merely be re- 
plotted with all abscissas changed proportionally to the varia- 
tion in the over-all drop, or the same curve could be used with 
suitable change in scale. 

(h) The resistances encountered vary about as the square of 
the velocity (as in Eq. 409), although probably the exponent 
should be slightly less than 2, say 1.8. Hence, doubling the 
velocity, to obtain a twofold rate of combustion, necessitates 
about four times as intense a draft, and nearly four times as much 
work will be done in moving the gases. 

(i) As the power is the product of resisting force by the velocity 
of motion, the amount required for removing the gases varies 
about as the cube of the velocity of flow, i.e., as the cube of 
the amount of air supplied, or as the cube of the rate of combus- 
tion. Thus, in order to double the rate of combustion, or boiler 
output, the draft-producing apparatus would have to do nearly 
eight times as much work. Therefore, while from the stand- 
point of space occupied by the boiler it may be desirable to 

* Bull. 21, U. S. Bureau of Mines, "Significance of Drafts," contains discussions 
of experiments on draft. 

t Thus it follows approximately Eq. (412). 



578 HEAT-POWER ENGINEERING 

force the rate of combustion as much as possible, the additional 
expense for power and apparatus for handhng the gases with 
greater velocity places a limit beyond which it is financially 
unprofitable to go. 

278. Amount of Pressure Drop Required, (a) The pressure 
drops (hf inches of water) generally needed for overcoming the 
resistance through the fuel bed have already been given in Fig. 
326 for the different rates of combustion of several sizes of 
various kinds of coal when burned under the usual conditions. 
But much variation from these curves exists, since the intensity 
of draft depends also on the thickness of the fuel bed, character 
of the ash and clinker, method of firing and other items. 

(b) The drop in pressure (hp inches of water) through the 
boiler passages depends on the length and cross sections of pas- 
sages, arrangement of baffles, arrangement of tubes, etc. Under 
ordinary rates of combustion it ranges as in Table XXIV and 
varies about as the square of the rate of combustion (as explained 
in Sect. 277 (f)) when operating at greater or lower rates. 

TABLE XXIV. — PRESSURE DROPS THROUGH BOILERS.* 

B. and W. — double deck 0.4 in. I Stirling or Heine 0.2 in. 

B. and W. — standard °-3 " I Return Tubular o.i " 

(c) To overcome the resistance of the breeching, or flues, be- 
tween the boiler and the stack, a pressure drop (hb) of about yo 
inch of water is generally assumed per 100 feet of length of smooth 
round passage when the boilers are being forced, and half as 
much for each elbow, though much depends on the mean hy 

draulic radius (-?r) of the passage, on the curvature of the bends, 

character of wall surface, etc. 

It would of course reduce the cost of the breeching if small cross 
sections and high velocity of flow were used. But since the re- 
sistance varies as the square of the velocity, greater draft would 
then be needed to overcome it, and this would, in general, add 
to the expense for the stack (or other draft-producing apparatus) 
an amount greater than the saving effected in outlay for the 
breeching. Hence, the breeching is usually given a liberal cross 
sectional area, one at least equal to that of the stack and gener- 
* Kingsley, Eng. Record, Dec. 21, 1907. 



DRAFT AND DRAFT APPARATUS 579 

ally 20 per cent greater, the velocity of flow being not more than 
that in the stack, and generally about 20 per cent less. 

(d) The total pressure drop (hi) inches of water between air 
inlet and base of stack evidently equals the sum of the drops 
through these various elements of the passage and of any 
others, such as those through economizers, which may be located 
between the boiler and stack. Thus hi == ^/ + ^p + ^6 + h^. 
The draft-producing apparatus should of course be proportioned 
to give a pressure drop at least sufficient to cause the greatest 
rate of combustion that will ever be demanded with the poorest 
fuel which is likely to be used ; then, smaller rates can be obtained 
by reducing the amount of air supplied, which can be done by 
regulating the dampers and air inlets either by hand or by some 
automatic device, the latter being generally operated by the 
slight variations in steam pressure which accompany the changes 
in the demand for steam. 

(e) The current of gases through the boiler can be caused 
either by " natural'' draft of a chimney (or stack), or by "arti- 
ficial " draft maintained either by steam jets or by power-driven, 
fans. 

The duty of the draft-producing apparatus is twofold — 
first, it must produce the needed intensity of draft and, second,, 
it must provide means for carrying off the products of combustion. 

279. Chimney Draft, (a) When one pound of carbon is com- 
pletely burned in air to CO2, the latter gas will have the same 
specific volume at the same temperature and pressure as did 
the oxygen with which it united (in accordance with Sect. 238 (a) ^ 
but the resulting flue gas will have one pound more material 
than was in the air which supplied the oxygen. Thus, for ex- 
ample, if the excess coefficient is two, 24 pounds of air with 
specific density = .0807 * are supplied for the complete combus- 
tion of one pound of carbon and there will result 25 pounds of 
gas, which will have a specific density* of (||) X .0807 = .084. 
Hence the weight of a column of air one foot high, at sea level 
and at temperature tf F., is 

D = (.0807 X 492) - (ta + 460), . . . (413) 

* Pounds per cubic foot at 32° F. (or 492° Absolute) and imder 14.7 povmda. 
square-inch pressure (measured at sea level). 



58o 



HEAT-POWER ENGINEERING 



and that of a similar column of flue gas, with excess coefificient 
equal two and with temperature tg° F., is 

d = (.084 X 492) -^ (/, + 460). . . . (414) 

(b) In Fig. 376 {a) the intensity of pressure exerted on the 
side of the partition X by the column {A) of cold air at tempera- 
ture ta, and that exerted by the equal column (G) of hot gas at 
tg° ¥., are respectively, in inches of water,* 

ha = .192 HD = 7.64 H/(ta + 460), . . . (415) 
and hg = .ig2Hd = 7. gsH/{tg -{- 460), . . . (416) 

where R is the height of the columns in feet, and D and d have 
the values given in Eqs. (413) and (414). This is of course on 



(a) 




Fig 376. 

the assumption that equal pressures of air are exerted on the 
tops of these columns. The difference between these pressure 
intensities on the opposite sides of the partition is (at sea level) 

7.64 7.95 \ 



(ha - hg) = H 



(417) 



^ta + 460 ta + 460/' ■ 

and, if the partition is removed, this will be the draft pressure 
tending to cause the flow of gases upward through column G. 

(c) If means are provided for maintaining the high temper- 
ature (tg) in column G, there will be a constant flow of gases, 
and as the air in column A is under atmospheric conditions the 
enveloping shell around that column can be omitted. Under 
these circumstances the conditions are those existing when a 
* See footnote, page 575. 



DRAFT AND DRAFT APPARATUS 581 

furnace and chimney (stack) are in operation, as in Fig. 376 (6); 
hence Eq. (417) can be used for obtaining the theoretical draft 
pressure ht developed by a stack of height H feet when the re- 
sistances through the stack are neglected, and it gives the draft 
pressure that would occur when the ash-pit doors are closed and 
no gases are flowing. 

Then, the theoretical height (Ht) of stack needed for producing 
a draft pressure of h inches of water at its base is (from Eq. 417) 

\ta + 460 tg + 460/ ^^ 

at sea level (14.7 lbs. per sq. in.). Both h and Ht will vary 
directly with the changes in the atmospheric pressure (barometer) . 

(d) Under normal conditions the temperature of the flue gas 
at the base of the stack generally lies between 500 and 600° F. 
in different types of boilers; but if "economizers " are used, it 
will be less and in some instances may be reduced to 300° F. 
When the boilers are being forced the temperature rises above 
the normal, which helps to augment the draft. In using Eqs. 
(417) and (418) for the draft and the height of a new stack, tg 
should be taken as the lowest flue temperature and 4 as the 
highest atmospheric temperature that are liable to exist simul- 
taneously. As the gases become cooled in passing up the stack, 
tg should be the mean temperature; it is customary, however, 
to use the temperature at the base of the stack and then to 
correct for the error, and for the resistances within the stack, 
by making the actual height about 25 per cent greater than the 
theoretical one. The effects of the column of hot gases above 
the stack and of the wind are generally neglected. Whether 
the wind assists or retards the draft depends on the arrange- 
ment of the chimney top. 

In practice the height of stack is from 80 feet, with free burn- 
ing coals and little resistance, to 175 feet, or more, with fine 
anthracite coal and with considerable resistance in the passages. 
But in settled districts the height should always be sufficient to 
satisfactorily dispose of the obnoxious gases. 

^e) The cross sectional area of the stack should, of course, be 
made ample for accommodating the gases when the boilers are 
forced to their maximum capacity, and in fixing the size allow- 
ance should always be made for any possible growth. 



582 HEAT-POWER ENGINEERING 

Having found the actual height of stack, it is quite common 
practice to compute the cross sectional area by using Wm. Kent's 
empirical formula, which was derived as follows: — 

Assuming that the volume of gas formed per hour is dependent 
on the amount of coal burned, which in turn is proportional to 
the boiler horse power (BP) developed, and that the velocity of 
flow varies as the square root of the height H (feet) of stack, it 
follows that the area is a function of BP -=- Vh. Then, from an 
analysis of numerous chimneys, Kent found that the effective 
area (E), in square feet, should be about 

E = .3(BP)-^Vh (419) 

It is also assumed that if it is considered that the chimney has a 
two-inch lining of stagnant gas, the flow through the remainder 
of the cross section can be taken as being without resistance. 
Hence the actual diameter of a circular chimney and the length 
of side of a square one are made four inches greater than the 
corresponding dimensions determined for the effective area. 

Kent's proportions are liberal as they provide for the com- 
bustion of about 5 pounds of coal per B. P. -hour, whereas not over 
4 pounds are ordinarily used. They allow for velocities of gas 
through the stack ranging from about 20 ft. /sec. with 100 feet of 
height to about 30 ft. /sec. in a 200-foot stack. 

(f) A more rational method of determining the proportions of 
a stack for a given set of conditions may be carried through. in 
the following order: 

1st. Assuming from 250 to 300 cubic feet of air at 60° F. as 
the amount needed to support the combustion of one pound of 
coal, and knowing the maximum weight of fuel to be consumed 
per unit of time, compute the corresponding total volume of gas 
at stack temperature. 

2d. Assuming a velocity of flow of from 20 ft. /sec, for short 
stacks, to 30 ft. /sec, or more, for very tall ones, compute the 
effective cross sectional area needed to discharge this volume; 
and then, allowing for a two-inch lining of stagnant gas, deter- 
mine the final dimensions of the cross section. 

3d. Find the loss of draft (^2 inches of water) arising from'the 
stack resistances, which are due to (a) change of direction of the 
gases upon entering the base of the stack, (b) the skin friction 
and (c) the displacement of the atmosphere by the issuing 



DRAFT AND DRAFT APPARATUS 583 

Stream. From Kingsley's experiments * this loss for a velocity 
V ft. /sec. was found to be given approximately by the equation 

hi = .00036 v~ (420) 

4th. Determine the pressure drop hi up to the base of the 
stack and compute the theoretical height (Hi) from Eq. (418). 
5th. Then find the actual height {H) of stack from 

H = Ht{hi + h2) ^hi (421) 

(g) By using the higher velocities, the stack diameter is de- 
creased, which would result in a reduction in the cost of the 
stack if other things remained the same; but these greater 
velocities necessitate an increase in the height of stack, thus en- 
tailing an additional expense which either partly or wholly 
offsets that saving. Evidently for a given set of conditions 
there is some velocity which will give a proportion of height to 
diameter requiring a minimum amount of material for con- 
structing the stack, and hence involving the least outlay of 
money. 

(h) For rough estimating it can be assumed that a 100-foot 
stack with gases at 500° and air temperature at 70° will exert a 
theoretical draft pressure of .6 inches of water at its base; that 
the draft varies directly with the height; and that the effective 
cross sectional area in square feet is equal to the number of 
pounds of coal burned per minute. For ordinary conditions 
with bituminous coal the stack area is about yth the grate area 
and with anthracite coal about Jth. 

(i) The different parts of a chimney and its foundation must 
not only carry the weights above but must also withstand the 
wind pressure. Chimneys are made of (i) common brick, (2) 
radial brick, (3) reinforced concrete and (4) steel plates. 

A comparison of Figs. 377 to 380, which illustrate stacks of 
the different types but of the same height and internal diameter, 
will show roughly the relative thickness, weight, extent of foun- 
dation and space occupied with the various constructions. 

(j) If made of ordinary brick (Fig. 377) the chimney must be 
lined at least for part of its height with fire brick so set as to 
have perfect freedom to expand or contract with temperature 

* Engineering Record, Dec. 21, 1907. 



584 



HEAT-POWER ENGINEERING 



,BR1CKCHIMNEY 
Fig. 377. 



n-^ 



24^ - 




RADIAL BRICK 
CHIMNEY 
8 ft. X 180 ft. 

rig. 373. 



DRAFT AND DRAFT APPARATUS 585 

changes. By using special radial brick (Fig. 378), composed of 
suitable material, and commonly made perforated, (i) the lining 
may be omitted, (2) the shell may be thinner and of lighter 
weight, and (3) the foundation may be smaller; besides which 
(4) the construction is better and (5) can be more rapidly done 
than with ordinary brick. The tallest chimney in the world is of 
this type. It is located at Great Falls, Mont., and is 506 feet 
high with 50 feet diameter at the top. 

(k) Many chimneys are now made of reinforced concrete (Fig. 
379), the steel reinforcing bars being arranged both circum- 
ferentially and vertically, the latter extending into the founda- 
tion, which is similarly strengthened. Such chimneys are (i) 
thinner than the brick, (2) weigh less, (3) occupy less space, 
(4) require but small foundations, (5) are free from joints and 
(6) can be rapidly constructed. The inner shell may be either 
of brick or reinforced concrete and in some cases is entirely 
omitted. 

(1) In order to withstand the wind, steel stacks are either 
guyed with wire or wire rope, or else have flared bases bolted to 
the foundation, in which case they are said to be self-supporting. 
They are preferably lined with brick to protect the metal from 
the heat and corroding action of the gases. The lining may 
either be self-supporting or else be constructed in independent 
sections each resting on a bracket extending from the steel shell. 
Such chimneys are (i) of light weight, (2) easily and rapidly 
constructed, (3) cost little, (4) occupy small space (except when 
flared) and (5) are free from air leakage if properly calked. 
They must be painted frequently to protect the metal from the 
weather and from the gases. 

280. Artificial Draft, (a) In a new power plant artificial draft 
apparatus is frequently employed as a substitute for a tall 
chimney, or to assist a short one, under the following conditions: 
(i) when the temperature of the stack gases is low, as when 
an economizer is used; (2) when the rates of combustion are 
high; (3) when fuels requiring intense draft are to be burned; 
(4) when certain stokers, like the underfed, are used; and (5) 
in certain other cases where in the long run it may be more de- 
sirable or more economical to purchase, operate and maintain 
such apparatus rather than have a chimney of large size. 



586 



HEAT-POWER ENGINEERING 



-5" 



REINFORCED-CONCRETE 

CHIMNEY 

8 ft. xl 180 ft. 

Fig. 379- 



STEEL I STACK 
8 ft. at 180 ft. 



Fig. 380. 



DRAFT AND DRAFT APPARATUS 



587 




Forced Draft. 



In an old plant it may be desirable to install artificial draft 
apparatus (i) to assist the original chimney when the plant has 
been increased beyond the capacity of the natural draft; (2) 
when it is desired to adopt unusual rates of combustion, or (3) 
to burn fuels requiring intense draft; (4) when there may be 
large emergency overloads or peak loads of short duration; and 
(5) when there are large 
and sudden changes in 
demand on the fur- 
naces. 

(b) In addition to 
its advantages in the 
instances already dis- 
cussed, the artificial 
draft apparatus is (i) 
easily installed; (2) is 
transportable and (3) 

occupies but little space; and (4) it also permits of careful adjust- 
ment of the air supply, which makes possible more perfect condi- 
tions of combustion. The regulation of air can be automatic, the 
controlling device being operated by the slight changes in steam 
pressure accompanying the varying demand on the boiler. 

(c) Artificial draft is 
produced either by steam 
jets or by power-driven 
fans, and when developed 
by the latter it is generally 
called mechanical draft. 

With forced draft (Fig. 
38 1 ) the ash pit is ' ' closed" 
(hermetically sealed) and 
the apparatus supplies it 
with air at a pressure 
above atmospheric (at a 
"plenum "); with induced 
draft (Fig. 382) the appa- 
ratus draws the gases from the boiler outlet, thus decreasing 
the pressure at that point below atmospheric; and with balanced 
draft these two systems are used in combination in a manner 
which will be discussed later. 




Fig. 382. — Induced Draft. 



588 



HEAT-POWER ENGINEERING 




Fig. 383- 



(d) Fig. 383 shows one of the many forms of steam jets used 
for forcing the draft. Somewhat similar devices can be placed 
in the base of the stack (as is universally done in locomotives) 

to produce induced draft. Such apparatus is 
relatively low in first cost, but is very wasteful 
of steam, using generally not less than 5 to 8 
per cent of the total steam generated, and it 
increases the stack loss because of the added 
moisture in the flue gas. Steam jets are conven- 
ient auxiliaries for meeting sudden or abnormal 
demands on the boilers, and the presence of the 
steam in the air supporting combustion tends to 

avoid the formation of clinkers. Fig. 384 shows a disc fan which 

is used in a similar manner. 

(e) With mechanical draft, the fans and their driving appa- 
ratus must be so designed as not to be affected by the dust, and 
with induced draft they must also be suitable for handling the 
hot gases without injury. If entire dependence is placed on fans 
for providing the draft, there should be duplicate (or auxiliary) 
apparatus installed to avoid plant shutdowns 
from failure of the draft apparatus. With 
a very short stack the fan equipment for 
forced draft costs roughly from 20 to 30 per 
cent as much as the equivalent brick chim- 
ney; while with induced draft the cost is 
about double that for forced draft as a larger 
fan ("exhauster") must be used because the 
gases are at high temperature. But though 
low in first cost, such apparatus depreciates rapidh^, involves 
considerable expense for attention and maintenance, and uses for 
power from i| to 5 per cent of the steam generated. 

(f) With forced draft the gas pressure within the boiler setting 
is above atmospheric, hence the tendency for hot gases and 
flames to issue through cracks in the walls and also to belch 
forth upon the opening of the fire doors. To avoid the latter 
occurrence the blast is shut off, usually automatically, when 
the doors are opened.* The air should always be introduced 
into the ash pit in such manner as to subject the fuel bed to 

* Some steamships using forced drafts have " closed firerooms " (stoke-holds) 
under pressure, and in such cases all leakage is into the interiors of the settings. 




Fig. 384. 



DRAFT AND DRAFT APPARATUS 589 

static pressure, or plenum, rather than to any localized blast 
action. 

With induced draft (either natural or artificial) the pressure 
within the boiler setting is below atmospheric, hence there may 
be detrimental infiltration of cold air through cracks in the set- 
ting and through the fire doors when opened. With this system, 
however, the fuel bed burns more evenly, and demands less 
attention than in the other, and it is not necessary to shut off 
the draft before opening fire and ash doors. Usually a by-pass 
flue is provided (as in Fig. 382) so that natural draft alone can 
be used for light loads, or in case of accident to the apparatus. 

With balanced draft the air is forced into the ash pit at suffi- 
cient pressure to become just atmospheric upon issuing from the 
surface of the fuel bed, and the gases are carried away from the 
combustion chamber by induced draft (either natural or arti- 
ficial) of such intensity as not to cause a decrease of furnace 
pressure below atmospheric. The proper balance between the 
forced and induced draft is usually maintained by some auto- 
matic device which regulates the two systems simultaneously. 
With balanced draft (i) there is no tendency for leakage either 
into or from the furnace; (2) the fire is not affected by opening 
the furnace doors for adding coal or "working" the fire; (3) it 
is possible to burn the smaller sizes of fuel, which are otherwise 
worthless, and which must be burned at high rates of combus- 
tion but cannot be used with forced draft because of their fine- 
ness; and (4) very high rates of combustion can be used with- 
out detriment to economy. 



CHAPTER XXXIII. 
GAS PRODUCERS AND PRODUCER GAS. 

281. Essentials of Producer-gas Apparatus. (a) Broadly 

speaking any apparatus in which gas is made is a ^' gas producer,'^ 
hut in engineering the term is almost exclusively applied to a 
class of apparatus producing gas largely by a process of partial 
or incomplete combustion. The gas made in such apparatus is 
known as "producer gas.'' 

(b) This gas has long been used for the heating of furnaces, 
the melting of metals, and a large number of similar purposes, 
but during the last twenty years it has come into particular 
prominence as a power gas, that is, a gas for use in internal com- 
bustion engines. It happens to be so constituted as to permit 
of high compression in the engine, thus giving high thermal 
efficiencies and, what is of greater importance industrially, it can 
,be made at the point of consumption more or less easily and very 
cheaply as compared with most of the other combustible gases. 

(c) Although the necessary apparatus differs considerably with 
the kind of fuel from which producer gas is to be made and with 
the purpose for which the gas is to be used, there are certain 
essential parts which generally exist in one form or another in 
all such apparatus. They are: (i) The fuel gasifier or "pro- 
ducer"; (2) some sort of "preheater" or "economizer"; (3) 
cleaning apparatus ; and occasionally (4) a gas storage reservoir 
of some kind, large or small. 

The first three parts are all shown in Figs. 5 and 391 to 394. 
In the particular types of plant shown in Figs. 5 and 391, the 
gas storage reservoir is practically nonexistent unless the pipe 
connecting the top of the scrubber with the engine cylinder be 
considered as partly serving that purpose. 

282. Simple Theory of Producer Action, (a) As indicated 
above, the ideal producer makes gas by what is known as par- 
tial or incomplete combustion. In its simplest conception this 

590 



GAS PRODUCERS AND PRODUCER GAS 



591 




Fig. 385- 



depends upon the combustion of carbon to carbon dioxide and 
then the reduction of this carbon dioxide to carbon monoxide 
by passing it over incandescent carbon. These reactions can 
be illustrated by means of Fig. 385. 

(b) Assume the vessel there shown to be 
filled with a column of carbon, the lower 
part of which is heated to incandescence. 
If air enter at the bottom of this fuel bed, 
as indicated by the arrows, its oxygen will 
unite there with carbon to form carbon 
dioxide, according to the equation (see Eq. 
(342a)) 

C + O2 = CO2 + 175,200 B.t.u., (423) 

which means that twelve pounds of carbon 

combine with thirty-two pounds of oxygen 

to form 44 pounds of carbon dioxide and that (12 X 14,600 =) 

175,200 B.t.u. are liberated per twelve pounds of carbon. 

(c) This carbon dioxide would then be reduced to carbon 
monoxide while passing up through the incandescent carbon 
above, and the reaction would occur according to the equation 

CO2 + C = 2 CO - 67,200 B.t.u. . . . (424) 

This means that the 44 pounds of carbon dioxide formed in the 
lower part of the fuel bed unite with twelve more pounds of 
carbon which will result in the formation of fifty-six pounds of 
carbon monoxide and the absorption of an amount of heat equal 
to 67,200 B.t.u., which quantity is easily obtained analytically 
in the manner described in the next paragraph. 

(d) Imagine the process occurring in two steps: First assume 
that the forty-four pounds of carbon dioxide break up into 
twelve pounds of carbon and thirty-two of oxygen. This could 
only occur with the absorption of 175,200 B.t.u., equal to the 
quantity liberated when the combination took place. Then 
imagine the carbon and oxygen to combine with an additional 
twelve pounds of carbon to form the fifty-six pounds of carbon 
monoxide. This would be represented by (see Eq. (343a)) 

2 C + O2 = 2 CO + 108,000 B.t.u., . . (425) 

which merely states that twenty-four pounds of carbon burning 
to carbon monoxide Hberate (24 X 4500 =) 108,000 B.t.u. 



592 HEAT-POWER ENGINEERING 

The first process involved the absorption of 175,200 B.t.u. in 
breaking up CO2, the second liberated 108,000 B.t.u. in 
the formation of CO, and the net result is the absorption of 
(175,200 — 108,000 =) 67,200 B.t.u., as given in Eq. (424).* 

(e) The composition of the gas formed and the thermal effi- 
ciency of the process can now be determined : — 

To produce the gas according to Eqs. (423) to (425), thirty- 
two pounds of oxygen are required per twenty-four pounds 
of carbon used and this oxygen will bring into the producer 
(32 X 77/23 =) 107. 1 pounds of nitrogen; hence the 163. i pounds 
of gas leaving the producer will contain this weight of nitrogen 
in mixture with the fifty-six pounds of carbon monoxide result- 
ing from the partial combustion, and will therefore have a com- 
position of about 34.4 per cent CO and 65.6 per cent N by 
weight. 

By volume the composition would be practically the same 
because the densities of CO and N are practically identical. 

283. Efficiency, Simple Producer Action, (a) Had the 

twenty-four pounds of carbon used in Sect. 282 (c) been burned 
directly to carbon dioxide, they could have liberated 24 X 14,600 
= 350,000 B.t.u. Burned to carbon monoxide they liberated 
only 24 X 4500 = 108,000 B.t.u. The difference, 

350,000 — 108,000 = 242,000 B.t.u., 

must be the quantity of heat which can be produced by subse- 
quently burning the carbon monoxide of the producer gas to 
carbon dioxide. This corresponds to 10,100 B.t.u. per pound of 
carbon. 

(b) If the thermal efficiency of the producer be taken as the 
ratio of the heat which can be obtained by burning the cold gas 
to the heat which could have been obtained by burning the 
original carbon, it is in this case 

^ Calorific Value of Gas ^ 242,000 ^ ^ . . 
" Calorific Value of Fuel 350,000 ^^^^ ^^ ^ 

Looked at in this way the process does not promise very well 
from a power-engineering standpoint. If the theoretical pro- 

* It will be shown in a subsequent paragraph that this treatment does not tell 
the whole story, but for a first analysis it is accurate enough. 



GAS PRODUCERS AND PRODUCER GAS 593 

ducer-efficiency is only 69 per cent, the real efficiency could 
hardly be expected to be more than 50 to 60 per cent, and, with 
thermal efficiencies of internal combustion engines ranging from 
20 to 30 per cent as an extreme value, the overall thermal effi- 
ciency of such a producer in combination with an engine would 
be low indeed. It will be shown later, however, that higher 
efficiencies are obtainable by modifying the process. 

(c) The efficiency given above is what is called the cold gas 
efficiency and is really not the correct efficiency to use under all 
conditions. For power purposes the gas must be cooled approxi- 
mately to room temperature before it can be advantageously 
used in an engine. This means removing all of the sensible heat 
given the material in the producer, and the cold gas efficiency 
is the proper value to use under such circumstances. 

(d) The process as outlined results not only in the production 
of 163 pounds of gas, which can liberate 242,000 B.t.u. when 
burned, but also in the liberation of 108,000 B.t.u. in the pro- 
ducer. In any real case part of this latter heat will of course be 
used to supply unavoidable radiation and similar losses, but the 
rest will raise the temperature of the carbon and of the air fed 
to the producer and of the gas formed. Hence the gas would 
actually leave the producer with a very high temperature, about 
2000° F. or more, and, by cooling it to room temperature, all of 
the heat liberated in the producer, and which was not lost by 
radiation or in other ways, could be obtained. 

The temperature rise resulting from the liberation of a cer- 
tain number of B.t.u. is equal to this number divided by the 
sum of the products of weight by specific heat of all the gases 
resulting from the combustion. The higher the temperature of 
the combustible gas and of the air before combustion, the higher 
will be the ultimate temperature attained.* Therefore, for fur- 
nace and similar work, where the object in burning the gas is to 
obtain high temperature, it is decidedly advantageous to have 
the apparatus located near the producer so that the sensible heat 
is not lost by radiation during transmission. 

For such purposes the thermal efficiency of the producer is 

* As the specific heats of gases increase comparatively rapidly at high tempera- 
tures, the temperature ultimately attained by any combustion will be lower than 
that given by the form of calculations suggested, as has already been shown. The 
error will be greater the higher the temperature attained. 



594 HEAT-POWER ENGINEERING 

correctly taken as the so-called hot gas efficiency, which is the 
quotient resulting when the sum of the total calorific value and 
the sensible heat of the gas leaving the producer is divided by 
the total calorific value of the fuel entering. Remembering that 
all heat which is liberated within the apparatus, and not lost by 
radiation and such, must be present in the gas leaving, the "hot 
gas efficiency " must be 

. _ Total Calorific Value of Gas -\- (Heat Liberated in Producer — Losses) . , x 
^^ " ' Total Calorific Value of Fuel ' ^^^^ 

and if all the losses in the case previously considered be assumed 
at 20 per cent of the heat liberated in the producer, the hot gas 
efficiency for this case would be 

_, 242,000 + (108,000 — 0.2 X 108,000) 

A/a — ■ ■ 

350,000 

328,400 



350,000 



93.5 per cent (approximately), 



a figure which is evidently much more promising than that pre- 
viously obtained. 

284. More Advanced Theory of Producer Action, (a) If the 

combustion processes indicated in the equations of the preceding 
section really occurred as there given it would be possible to 
pass a stream of carbon dioxide into one end of a tube containing 
hot carbon and have nothing but carbon monoxide issue from 
the other end. Experiment, however, shows that this is impos- 
sible, for, no matter what the conditions are, there will always be 
a certain amount of carbon dioxide mixed with the issuing carbon 
monoxide. 

(b) Experiment further shows that, other things being equal, 
the higher the temperature in the tube the greater will be the 
proportion of carbon monoxide in the gas issuing, and the lower 
the temperature the greater will be the proportion of carbon 
dioxide. 

(c) This is explained chemically by what is called " chemical 
equilibrium." Briefly, if no other variables need be considered, 
at each given temperature, there are certain definite proportions of 
carbon monoxide and carbon dioxide which will be in equilibrium 
with carbon. If a mixture of these gases in other proportions is 



GAS PRODUCERS AND PRODUCER GAS 



595 




Diagram 
bon Monoxide, Carbon Dioxide 
and Carbon at'Atm. Pressure 



900 1000 
Temp." C. 

1652 1832 
Temp.°F 

Fig. 386. 



1100 
3012 



1200 
2192 



brought into contact with carbon, reactions will occur and con- 
tinue until the equilibrium proportions corresponding to the 
given temperature are attained.* 

(d) This equilibrium is well shown by the diagram of Fig. 386 
which is plotted from experimental results obtained with carbon in 
a tube, as described in (a) of this section. In this figure the abscissas 
represent temperatures 
in Centigrade and Fah- 
renheit degrees and ordi- 
nates represent per cent 
of CO by volume. Sub- c 
tracting these ordinates "^ 
from 100 gives the per- 
centages of CO2, which 
are evidently shown to 
scale by distances from 
the curve to the 100 per 
cent line. 

The curve shows that for low temperatures probably a very 
small amount of carbon monoxide would be found to be issuing 
from the tube in the experiment described above, while at high 
temperatures it shows the issuing gas to be composed almost 
entirely of carbon monoxide. 

(e) In giving the effect of temperature on the composition as 
deduced from experiment, it was limited by the phrase "other 
things being equal." Experiment shows that the pressure at 
which the gases exist also has a certain effect upon the compo- 
sition. The higher the pressure the greater the percentage of 
carbon dioxide in the equilibrium mixture at any temperature. 
Pressure variations are, however, so slight in producer work that 
their effect may be safely neglected. 

(f) The time of contact is also of great importance. Chemical 
reactions do not occur instantaneously (that is, in time measured 
in infinitesimals) and the reactions in question, which lead to the 
equilibrium conditions plotted in Fig. 386, take a very appreciable 
time for completion. The higher the temperature the shorter the 
time necessary for the attainment of equilibrium conditions. 

* Whether reaction then ceases, or whether counterbalancing reactions which 
do not further change the proportions of carbon monoxide and carbon dioxide 
continue, is a matter of indifference for the present discussion. 



596 



HEAT-POWER ENGINEERING 




10 60 80 100 120 
Time of Contact, Seconds 



Fig- 387- 



This is well shown in Fig. 387 which gives results obtained in 
experiments with carbon in the form of charcoal. In the figure 
each curve is an isothermal; that is, it shows the proportions of 
carbon monoxide and of carbon dioxide that will exist after 
gas, which was originally all carbon dioxide, has been in contact 
with carbon at a certain temperature for different lengths of time. 

As before, the ordinates 



represent percentages of 
CO and the distances from 
the curve upward repre- 
sent percentages of CO2. 
It will be observed that, 
while it takes a time 
period of from 120 to 
160 seconds to attain ap- 
proximate equilibrium at 
8oo°C. (as shown by the tendency of the curve to become hori- 
zontal at this point), it requires only 5 seconds to attain equi- 
librium with a very much higher percentage of CO at 1100° C. 

(g) The effects of both time and temperature are well shown in 
Fig- 389, in which the three coordinates are time, temperature 
and volume per cent, of / 

CO. The curves shown 
are those of Fig. 387, 20- 
but here each curve is 
located in its own tem- o' 

o 

perature plane. A sur- ^eo 
face can be imagined 
as passed through these 
curves and the coordi- 100 ■ 
nates of any point in 
it will show the relative 
percentages f of CO and CO2; 
after any period of contact. 

(h) Unfortunately the surface condition of the carbon has an 
effect upon the time required for the attainment of equilibrium. 
In general the more porous the carbon, and the smaller the 
lumps, the shorter will be the time required to attain the equi- 
librium corresponding to the given temperature. This is just 
what would be expected, as carbon of porous character and in 




which result at any temperature 



GAS PRODUCERS AND PRODUCER GAS 



597 



small lumps will expose most surface on which the reaction may 
occur. 

The effect of surface (and possibly other) conditions is shown 
by a comparison of Figs. 387 and 388. The full lines in the latter 
represents the results of experiments made with carbon in the 
form of coke in lumps about the same size as those of the char- 




£C=Temperature, 



Fig. 389. 



coal used in obtaining the results shown in Fig. 387. The dotted 
lines show similar curves for anthracite under approximately 
like conditions. 

The curved surface shown in Fig. 389 is then only one of a 
number which differ in curvature with the character of the carbon. 
The more porous and the smaller the lumps the sharper will be 
the rise of the curves as they leave the temperature axis at the 
front, and the sooner will they become flatter as they recede. 



59o HEAT-POWER ENGINEERING 

(i) The preceding discussion is purely theoretical and leads 
to the following conclusions: For best producer operation (that 
is, the manufacture of gas containing the maximum amount of 
carbon monoxide and the minimum amount of carbon dioxide 
and nitrogen) the requirements are : — 

(i) High temperature within the producer; 

(2) Long time of contact between entering air, gas in process 

of formation, and hot carbon; 

(3) Maximum porosity and minimum size of fuel; 

(4) Theoretical air supply. 

285. Practical Limitations, (a) In the real producer there are 
a number of practical considerations which materially modify 
the conclusions just given for the theoretical case. For instance, 
all real fuels contain ash and this will fuse and form clinker if 
the temperature becomes high enough.* Such clinker is very 
undesirable because it obstructs the gas passages between the 
lumps of fuel, making it difficult or impossible for gas to flow 
through certain areas. This results generally in more violent 
combustion in the parts of the bed which are still unobstructed, 
and this localized combustion materially augments the trouble 
by raising the temperature locally and causing the rapid forma- 
tion of more clinker. The more or less complete obstruction of 
the gas passages will ultimately make continued operation im- 
possible. Clinker also gives considerable trouble by fusing to 
the walls of the producer itself. 

Thus, in actual operation, the fusing temperature of the ash 
sets the limit to the temperature allowable in the producer and 
this temperature varies considerably with different fuels; but, 
with those adapted to use in present-day producers, the tem- 
perature can generally be carried at such a value as to give a 
theoretical proportion of from 96 to 98 per cent of CO (with 4 to 
2 per cent of CO2) by volume in the issuing gas. 

(b) Caking fuels also cause trouble in producer operation. 
The coalescence of the individual lumps decreases the percentage 

* A number of experimenters are now operating producers at what are ordi- 
narily considered exorbitantly high temperatures, by mixing with the coal some 
cheap material, such as limestone, which acts on the ash as a flux. The ash is thus 
made very fluid and is drained off just as it is in the case of blast furnaces. Several 
plants of this character are said to be in successful operation in Europe but they 
have not yet been commercially adopted in this country. 



GAS PRODUCERS AND PRODUCER GAS 599 

of voids in the fuel bed and thus obstructs the flow of gas. It 
also assists in causing "arching " so that the lower part of the 
fuel column may burn to ash and drop down while the upper 
part remains suspended above. Constant or intermittent stir- 
ring of the fuel bed (often combined with the maintenance of a 
fairly low temperature) are necessary with such fuels, although 
both stirring and low temperature have a detrimental effect upon 
the gas made. Stirring is often improperly done, and opens up 
fairly large free passages through the bed, thus allowing CO2 
and even air to pass through without coming into intimate 
contact with hot carbon. 

(c) The theoretical requirement of long time of contact is more 
or less a relative consideration, as previously indicated ; and the 
length of time needed was seen to depend both upon the tempera- 
ture and upon the physical character of the fuel. 

Remembering that a producer operates with a continuous flow 
of gas through the fuel bed, the time of contact between gas and 
carbon must be measured in the actual case by the length of 
time it takes a given particle of gas to pass through the fuel bed, 
and hence depends on the velocity of the gas passing through 
the producer and the length of the passage through the bed of 
fuel. 

There is a practical limit to the allowable depth of fuel bed with 
any given fuel, in any given size, with any given type of pro- 
ducer. This limit is set by the difference of pressure necessary 
to cause flow through the bed. The length of the gas path 
through the producer being thus limited, the time of contact 
varies with the velocity which, in turn, depends on the diameter 
of the fuel bed. Large diameters will correspond to low veloci- 
ties and long times of contact; small diameters will correspond 
to high velocities and short times of contact. 

(d) This consideration would indicate a large diameter of 
producer to be desirable in every case, but there are two practical 
limitations which must be recognized: (i) The cost of the in- 
stallation will increase as the size of the apparatus required per 
horse power increases; and (2) there will be difficulty in operat- 
ing the producer under light loads, for when a producer which 
is of suth diameter as to have a low gas velocity at full load is 
operated at a small fraction of that load, the small amount of air 
passing through may not be sufficient to keep the temperature 



6oo HEAT-POWER ENGINEERING 

of the large bed of fuel up to that necessary for the formation 
of a high percentage of carbon monoxide. 

The diameter of any given producer must therefore be a com- 
promise between the large value desirable at full load and the 
smaller value which is desirable at light load and which involves 
less expenditure for equipment. 

(e) Practice has shown that certain proportions are advisable 
with certain types of producers and certain kinds of fuel. In 
general it may be said that producers are built of such diameters 
that the amount of fuel gasified when carrying rated load is 
from 10 or 12 pounds per square foot of cross section of fuel bed 
per hour in the simpler types, up to 30 to 40 pounds per square 
foot per hour in the more complicated types of producers oper- 
ating on particularly suitable fuels. The overload capacity is 
determined by the blast pressure available, by the clinkering 
temperature of the ash and the fusing or fluxing temperature of 
the producer lining. 

(f) In the purchase of fuel, porosity can hardly be considered 
except in a general way, it being merely incidental to other con- 
siderations. The size of lumps can, however, be taken into 
account both as to effect on the operation of the producer and 
on the price, the smaller sizes generally costing less than the 
larger. The smaller the size of the fuel, with a given depth of 
column, the greater the difference of pressure required to pass 
the necessary volume of gas through the producer; and with a 
given maximum blast pressure, the lower is the capacity of a 
producer, if the same depth of column is maintained. Given 
a certain difference of pressure it is of course possible, by de- 
creasing the length of path through that bed, to make any given 
quantity of air enter the bed per square foot of section in a given 
time; but this detrimentally shortens the time of contact or 
else necessitates an increase of diameter in order to reduce the 
velocity of flow to a satisfactory value. 

Furthermore, with very small sizes the necessary velocity in a 
producer of a given diameter may be so great that parts of the 
fuel will be picked up by the gas and be carried out of the 
producer. This occurs to a greater or less extent with every 
producer in actual operation. Finely divided ash or a certain 
amount of finely divided or powdered fuel is practically always 
carried out by the issuing gas. 



GAS PRODUCERS AND PRODUCER GAS 6oi 

The larger the size of fuel the greater are the voids, hence the 
passages through the fuel bed are of greater cross section and 
the allowable velocity and blast pressure are less, but smaller 
surfaces are exposed for reaction. 

(g) There are thus practical limits to the largest and smallest 
sizes of fuel which can be satisfactorily used in any given case. 
Sizes commonly used vary from about eight inches in diameter 
to pea anthracite. The larger sizes are generally mixed with 
smaller ones to decrease the passage areas in the fuel bed, while 
the smaller sizes very often have the finer particles screened out 
to increase the free areas. 

(h) Lastly, practically no producer can be operated with the 
theoretical air supply. In order to supply the amount of oxygen 
necessary to produce the required quantity of CO (and the CO2 
which must necessarily accompany it), air in excess of the the- 
oretical requirement must be passed through the producer. In 
general the smaller the size of fuel and the lower the velocity, 
the smaller need this excess be, but it can never be entirely 
eliminated. As a result, producer gas practically always con- 
tains more or less free oxygen and consequently an excessive 
amount of nitrogen. The typical analyses of producer gases in 
Table XXV show this. 

286. Artificial Cooling of Producers (General), (a) In con- 
sidering the difference between cold gas and hot gas efficiencies, 
it was shown that a large amount of heat in excess of that re- 
quired to supply radiation and similar losses must be liberated 
within a producer by the very process to which the formation 
of producer gas is due. In actual producers using any of the 
ordinary fuels, the excess heat would quickly raise the temper- 
ature to a prohibitively high value. Clinker troubles would 
assume such magnitudes as to entirely prevent successful oper- 
ation and in many cases there would even be danger of fusing 
the refractory lining of the producer shell. 

(b) To prevent such difficulties producer operation is modi- 
fied in several different ways by introducing some heat absorb- 
iilg process to lower the operating temperature. Part of the 
excess heat is absorbed naturally to a certain extent with all 
real fuels, for they contain hydrocarbons and water which are 
vaporized (and to a certain extent modified chemically) at the 



6o2 



HEAT-POWER ENGINEERING 







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GAS PRODUCERS AND PRODUCER GAS 603 

temperatures attained; but it is only with exceptionally wet 
fuels, such as poorly dried peat, that enough heat is absorbed in 
this manner to make operation practical. The reduction of tem- 
perature due to the presence of CO2, nitrogen and moisture in 
the air (from the atmosphere) is also slight. Hence in actual 
operation it is necessary to have some artificial means of cooling. 
(c) Two methods of artificially controlling the temperature are 
in use. They may be called 

1. The "Carbon Monoxide" Method, in which burned pro- 
ducer gas is returned to the producer in mixture with the air 
supply, and absorbs heat largely by the reduction of contained 
CO2 to CO; and 

2. The Water Vapor Method, in which water vapor is mixed 
with the air supply and absorbs heat by reduction in contact 
with hot carbon. 

The details of these two methods are considered in the follow- 
ing sections. 

287. The " Carbon Monoxide " Method of Temperature Con- 
trol, (a) Burned producer gas may be roughly said to consist 
of carbon dioxide and water vapor, mixed with nitrogen. Re- 
turning such material to the producer will effect cooling in two 
distinct ways: (i) The carbon dioxide passing over heated car- 
bon will be more or less completely reduced to carbon monoxide; 
and (2) the water vapor in contact with hot carbon will be 
more or less completely broken up to form hydrogen, carbon 
monoxide and carbon dioxide. 

(b) Under ordinary circumstances the first way will be the 
only one of appreciable magnitude because of the small amount 
of water vapor generally present when this method of cooling 
is used. The quantity of carbon dioxide which must be returned 
in order to maintain a given temperature in a theoretical case 
can be approximately determined if the amount of carbon dioxide 
and carbon monoxide which will be in equilibrium at that tem- 
perature and the amount of heat which must be absorbed to 
maintain the desired temperature are known. Knowing the 
amount of heat (see Eq. 424) which is absorbed for each unit 
weight of carbon present in carbon dioxide when the latter is 
reduced to monoxide, it is possible to determine how much 
carbon dioxide will have to be reduced and how much carbon 



6o4 



HEAT-POWER ENGINEERING 



monoxide will result. It is then only necessary to find the 
amount of carbon dioxide which will be in equilibrium with this 
CO, to add this amount to that used in forming the monoxide, 
and the result is the total quantity of carbon dioxide which 
must be thus returned. 

(c) It is interesting to note that nearly all carbon returned in 
the form of carbon dioxide is used repeatedly, being reduced to 
carbon monoxide in the producer, burned to dioxide in the ap- 
paratus utilizing the gas, and returned to the producer again 
for reduction, and so on. Hence the carbon furnished by the 
fuel will be less than the total carbon in the issuing gas by just 
the amount which is thus used over and over again. It should, 
however, be noted, that there is a natural limit to the amount 
that can thus be used. The carbon dioxide can be reduced to car- 
bon monoxide only with the absorption of heat and this heat can 
come only from fuel carbon burned in the producer. The method 
is then simply one which results in the entrapping in available 
form of some of the heat which would otherwise be wasted. 
The actual amount of carbon which can thus be used repeatedly 

in any given case is com- 
paratively small and the 
principal advantage of 
the process lies in the 
temperature control and 
uniform composition of 
gas (see (d) below) rather 
than in the saving of fuel. 
The operation of arti- 
ficially cooled producers 
is shown diagrammati- 
cally in Fig. 390 (b) in 
comparison with the uncooled method of operation shown in 
Fig- 390 («)• The way in which more heat is made available at 
the expense of what would otherwise be lost is well shown by the 
width of the various streams. 

(d) The fact that the time of ignition in internal combustion 
engines should ordinarily be varied with the composition of the 
fuel was mentioned in Sect. 212 (h) . When gas is made in a pro- 
ducer controlled by the carbon monoxide method its composi- 
tion is remarkably uniform from light loads to full loads, hence 




Heat Value ot 
C Supplied to 
Ibe Producer 



Heat abaorbing 
jower of material 



Fig. 390. 



GAS PRODUCERS AND PRODUCER GAS 605 

the time of ignition can remain fixed without danger of large 
variations in thermal efficiency. This must be considered an 
advantage possessed by this process in comparison with that 
considered below. 

288. The Water Vapor Method of Temperature Control, (a) 

Experiment shows that when steam is passed over incandescent 
carbon a certain amount of hydrogen is released, that the oxygen 
previously combined with it unites with some of the carbon to 
form carbon monoxide and carbon dioxide,* and that some of 
the steam will still remain unchanged regardless of the tempera- 
ture attained and of the amount of carbon present. It is again 
a case of chemical equilibrium similar to that considered in 
Sect. 284 and the resultant composition will depend largely on 
the temperature. 

No matter what the temperature is, a certain amount of heat 
will be absorbed in the process of decomposing the water and 
this is always greater than that liberated by the combination of 
liberated oxygen with carbon to form either CO or CO2. Hence, 
the process, when used in a producer, must result in lowering the 
producer temperature, and by properly proportioning the amount 
of steam per pound of air the temperature can be directly con- 
trolled. 

(b) The gas made by this process will contain hydrogen, and 
a small amount of methane as well as carbon monoxide, as a com- 
bustible constituent; and since all of the hydrogen and some 
of the carbon monoxide were formed in such a way as not to 
necessitate the introduction of nitrogen, there will be a smaller 
percentage of nitrogen in the resulting gas than when made by 
either of the processes previously described. The gas may, in 
fact, be considered as made by the theoretical process outlined 
in Sect. 282, with an admixture of hydrogen, carbon monoxide 
and a small amount of carbon dioxide, all resulting from the 
action of the steam. 

(c) As a result of the presence of the hydrogen and of carbon 
monoxide not accompanied by its proportion of nitrogen, the 
calorific value of gas made by this process is higher than that 
made by those previously described. 

(d) One of the disadvantages of this process is that the com- 

* A small amount of methane, CH4, is also found in all cases. 



6o6 HEAT-POWER ENGINEERING 

position of the gas is very changeable, the hydrogen content 
increasing from a very small amount at light loads to very large 
ones at heavy loads. This necessitates a constant shifting of 
the time of ignition if a uniformly high thermal efficiency is 
to be obtained, — the ignition occurring earliest with minimum 
hydrogen content. Such constant shifting with rapidly varying 
load is, however, not practicably attainable, hence the engine is 
apt to operate at widely varying efficiencies, and, in extreme 
cases, may not even operate satisfactorily, 

(e) There are also many methods of applying this process 
which give poor results because of the method rather than the 
intrinsic nature of the process. Any method of controlling the 
steam supply which depends only on the instantaneous load on 
the engine must cause unsatisfactory operation in the following 
way: During a period of very light load the fuel bed has a ten- 
dency to cool down and if continued for any great length of time 
the temperature drop will be serious. Imagine full load to be 
demanded suddenly after such a period. The fuel bed tempera- 
ture is hardly high enough to make the necessary quantity of 
monoxide, and if the producer is fitted with a device which will 
immediately throw on full steam supply with demand for full 
load, the fuel bed will be still further cooled by the deluge of 
water vapor. Many failures of otherwise successful producers 
have been due to just such actions. 

Forms of steam control which depend upon the temperature 
of the gas issuing from the producer, or the equivalent of this, 
seem to give better results. 

(f) The fact that water must be vaporized before it can be 
mixed with the entering air is often taken advantage of to con- 
serve some of the sensible heat in the gas leaving the producer. 
An apparatus variously known as a vaporizer, an economizer, or 
by several other names, is so arranged that these gases, while 
passing through or around it, heat and vaporize water contained 
within it. Somewhat similar devices also called economizers, 
or, more correctly, preheaters, are often arranged to preheat the 
air on its way to the producer so that it may pick up more water 
vapor and also return to the producer some of the heat that 
would otherwise be wasted. 

The upper part or cover of the producer shown in Fig. 5 forms 
a vaporizer, the vapor being picked up by the air supply as it 



GAS PRODUCERS AND PRODUCER GAS 607 

passes over the surface of the water. A somewhat similar de- 
vice is shown in Fig. 393. Other forms, better known as econo- 
mizers, are shown in Figs. 391 and 392. 

289. Effects of Hydrocarbons in Fuels, (a) The behavior of 
■real fuels in producers and the composition of the resulting 
gases are much modified by the presence of volatile hydrocarbons. 
These are distilled off within a producer and are very muck 
modified by the high temperature of the heated fuel and refrac- 
tory material before finally issuing with the gas. 

(b) The tendency of all such mixtures of hydrocarbons when 
heated is to undergo changes, yielding carbon, hydrogen and 
new hydrocarbons, some of which are more volatile than the 
originals and others less volatile. If heating is continued long 
enough and at a sufficiently high temperature the ultimate prod- 
ucts are practically hydrogen, methane and carbon (lampblack). 
The hydrogen and more volatile hydrocarbons, such as methane, 
form desirable constituents of the producer gas * and the carbon 
can be gasified if it remains in the producer, or it is compara- 
tively easily separated if it passes out with the issuing gas. The 
less volatile hydrocarbons, however, if allowed to issue with the 
gas, will subsequently condense, giving a thick, viscous, or semi- 
solid material known either as tar or pitch, depending upon its 
composition and consistency. Such material is apt to cause 
pipe stoppages, to clog the gas cleaning apparatus, the engine 
valves and such. 

(c) With anthracite fuels the amount of tar formed is com- 
paratively small and gives little trouble as it is easily separated 
from the gas. Bituminous fuels, on the other hand, yield large 
quantities of tar if used in producers of the simpler kinds. 
Such tar must be separated from the gas if the latter is to be 
transported any distance from the producer, or is to be used in 
internal combustion engines or in any apparatus requiring it to 
flow through small orifices. This elimination not only entails 
the use of more or less costly apparatus, which generally con- 
sumes power, but also results in lowered thermal efficiency, as 

* This statement is true as far as definite knowledge goes at present, but it 
seems probable that under certain conditions some of the products may prove 
undesirable because of chemical instability leading to spontaneous ignition at low 
compressions. 



6o8 



HEAT-POWER ENGINEERING 



the calorific value of the separated tar represents, in many cases, 
a considerable portion of that of the original fuel. 

(d) The most successful method of elimination so far produced 
depends upon the destruction of the tar within the producer. 
This is accomplished by passing the tar forming vapors (dis- 
tilled off the freshly charged fuel) through an incandescent 
fuel bed before leaving the producer. The process taking place 
is called cracking and results in the formation of hydrogen, 
methane, small quantities of other very volatile hydrocarbons 
and solid carbon. The solid carbon largely remains within the 




Gas to Dry Scrubber 
— *■& Engine or direct 
to Bhigine 



i^^ 



Fig. 391. — Up Draft Suction Producer. 



producer bed and is subsequently gasified, while the hydrogen 
and other products of the cracked hydrocarbons pass off with 
the gas. 

(e) This process can be carried on in an ordinary up draft 
producer operating much like that of Fig. 391, but modified so 
that, while the gas to be used is drawn off from the top of the 
main fuel column, the volatiles distilled off from the top of the 
freshly charged fuel in the extended hopper are piped around 
and introduced with the air entering at the bottom. This 
method has not met with great commercial success, although 
it is used to some extent in Europe for large installations. 

(f) Another and a very successful method is to reverse the 
direction of flow of gas through the producer, introducing air 



GAS PRODUCERS AND PRODUCER GAS 



609 




6io 



HEAT-POWER ENGINEERING 



and fuel at the top and removing gas at the bottom. This gives 
what is known as a down draft producer, one example of which 
is shown in Fig. 392. In this particular type, a bed of coke is 
ignited upon the brick arch which forms the grate, and the bitu- 
minous coal is fired upon this from above. 

(g) Few of the down draft producers so far constructed have 
permitted of continuous operation because of the difficulty of 
removing the ash and clinkers without shutting down the pro- 
ducer. They are, therefore, generally operated intermittently, 
say for a week, after which they are cleaned out and restarted. 
The type shown in Fig. 393, which is known as a water bottom 



Air^upply. 




Fig. 393. — Down Draft Producer, Continuously Operated. (Akerlund Type.) 



producer (see next section), overcomes this difficulty and per- 
mits of continuous operation. 

(h) To circumvent the difficulties met in attempting to gas- 
ify bituminous and similar fuels in up draft producers, the 
so-called double zone type of producer is also used. One exam- 
ple of this type is shown in Fig. 394. This producer may 
be regarded as a down draft producer superimposed upon one 
of the up draft kind. Air enters both top and bottom and 
gas is drawn off near the middle of height. The only draw- 
back is the necessity of carefully watching operations so that 
the upper incandescent zone may remain extensive enough to 
successfully crack the hydrocarbons and so that the combus- 
tion below the "gas offtake " may occur at just the proper rate 
to completely gasify all the coked material coming down from 
above. 



GAS PRODUCERS AND PRODUCER GAS 




6l2 



HEAT-POWER ENGINEERING 



"Watsr Sealed Charging Hopper 
Is brought over diiferent parta 
"''*"l!by-rotatmg top 

r Sealed Sight 
alrd J>oke Hole 




Fig- 395- 



290. Water Bottom and Grate Bottom Producers, (a) No 
matter what the type of producer, the column of fuel must be 
supported in some way. Producers are divided roughly into 
two types depending upon the way in which the fuel bed is 
supported. Producers arranged like those in Figs. 393 and 394, 

in which the bed of fuel is 
supported on a pile of its own 
ash, resting in a saucer shaped 
depression filled with water, 
are called water bottom pro- 
ducers. The shell of the pro- 
ducer must dip into the water 
by a sufficient amount to 
prevent the passage of air 
into the producer, or the 
escape of gas out of the pro- 
ducer, under the action of the 
greatest difference of pressure 
which will ever occur during 
operation. 

Producers of this kind possess the great advantage of permit- 
ting the convenient withdrawal of ash at any time during opera- 
tion. They also dispense with almost all of the metal work 
found in other types at the bottom of the fuel column where the 
temperature is apt to become dangerously high if attendants 
are careless and where the rough work 
and sharp ash and clinker cayse rapid 
depreciation. 

(b) Producers in which the column 
of fuel is not supported by ashes in a 
water sealed saucer may be roughly 
grouped under the head of grate bottom 
producers. Examples are shown in 
Figs. 391, 392, 395 and 396. The grates may be of any degree 
of complexity from the simple grid of cast iron bars or of plain 
iron pipes, or the arch of fire brick shown in Fig. 392, to the most 
complicated of mechanical grates, such as the rotating and scrap- 
ing devices shown in Figs. 395 and 396, or a rocking grate much 
like that used under steam boilers, as shown in Fig. 391. 

(c) Mechanical grates, operated continuously by power in 




Fig. 396. 



GAS PRODUCERS AND PRODUCER GAS 613 

large sizes and intermittently by hand in small ones, are decidedly 
advantageous. They make possible the easy working down of 
ash and clinker, which in other cases would have to be barred 
down by poking from above, from the sides and through the 
bottom. When continuously in motion they tend to maintain 
uniform conditions within the producer, shaking the fuel column 
sufficiently to keep it open, to work down ash and to break up 
clinker. 

Combined with a depth of ash sufficient to seal against leak- 
age in or out, or with a water bottom, they afford ideal operating 
conditions. 

291. Induced Draft and Forced Draft, (a) In developing the 
theory of the producer it was assumed that air could be made 
to enter and the resultant gas to leave. This flow can only be 
produced by maintaining a difference of pressure between inlet 
and outlet orifices. Two distinct methods are used for creating 
flow in this way. In one the pressure on the entering side is 
raised above that of the atmosphere; that is, air is pumped into 
the producer. Such producers, which are operated under what 
corresponds to forced draft in boiler practice, are called pressure 
producers. The pressure of air and gas within the producer is 
greater than the atmospheric pressure outside of the producer 
shell by the amount necessary to cause flow through the pro- 
ducer and all subsequent apparatus. One great disadvantage 
of such types is the fact that a leak anywhere in the apparatus 
results in the outflow of poisonous producer gas. Opening of 
poke holes for inspection of the fire or for stirring up the bed 
will result similarly. For such reasons pressure producers must 
always be operated in well ventilated structures, preferably with- 
out side walls where climatic conditions permit. 

Air is generally pumped into such producers by a steam jet 
blower similar to that shown in Fig. 395. With proper propor- 
tions the amount of steam can be regulated so as to just equal 
that required for cooling the producer by decomposing in con- 
tact with the hot carbon. In general this steam must be under 
so high a pressure that a separate boiler is necessary for its gen- 
eration, but in large plants this is not a great disadvantage. In 
some types the steam is generated in a vertical water tube boiler 
which receives the hot gas coming from the producer. In this 



6l4 HEAT-POWER ENGINEERING 

way part of the sensible heat in the gas is returned to the fuel 
column. 

Any other form of air pump can be used; a very common 
one is that shown at the right In Fig. 394. As shown it is used 
as an exhauster, but an exactly similar device can be used as 
a blower, the only difference being in its location and method of 
connection. 

(b) The other method of operation referred to above causes 
flow through the producer and subsequent apparatus by lower- 
ing the pressure at the outlet to a value below that of the sur- 
rounding atmosphere. Atmospheric pressure at the inlet is then 
sufficient to cause flow. Such producers, operated under condi- 
tions corresponding to induced draft in boiler practice, are known 
either as induced draft producers or as suction producers, depend- 
ing upon the apparatus used for reducing the pressure. 

When an exhauster like that in Fig. 394, or any similar appa- 
ratus, is used the producer is called an induced draft apparatus; 
when a gas engine operated by the producer draws its own 
charge through the system by lowering the pressure during each 
suction stroke as shown in Fig. 391, the apparatus is called a 
suction producer. 

(c) One great advantage of all induced or suction draft sys- 
tems is that any leak always results in the flow of air into the 
apparatus rather than escape of gas out of the apparatus. Such 
air may, in extreme cases, furnish oxygen sufficient to burn an 
appreciable quantity of the gas within the apparatus, as for in- 
stance in case the leak is immediately above the fuel bed in the 
producer where the gases still have a high enough temperature to 
ignite, and this would result in a diminished output of power gas, 
but could not ordinarily endanger human life. A leak at a point 
beyond the producer would result in the mixture of air and cold gas 
which could be entirely counterbalanced by the admission of less 
air to the apparatus in which the gas is subsequently burned. 
However, such mixtures of air and gas within the apparatus 
represent a possible source of trouble as they may sometimes 
acquire explosive proportions and there is always the possibility 
of ignition. The high pressures resulting from explosions would 
endanger the apparatus and possibly human life, but can easily 
be guarded against by providing some form of pressure relief 
such as a water seal or large flat door, or plate, with minimum 



GAS PRODUCERS AND PRODUCER GAS 



615 



inertia so as to permit of rapid opening with minimum pressure 
rise. 

(d) There are a few types of producer plants so constructed 
that they operate on what is known as a balanced draft. This is 
generally achieved by using the equivalents of one blower and 
one exhauster. The combined action of the two is such that 
the pressure within the producer itself is not greatly different 
from atmospheric, that on the outlet side being generally main- 
tained at a value equal to atmospheric. The dangers associated 
with leakage in or out are thus minimized. 




292. Mechanical Charging, (a) Most of the producers used 
in power plants are charged by hand, particularly in the smaller 
sizes. With small producers the shell is generally made of such 
depth that it will hold sufficient fuel 
for from three to six hours' operation 
without recharging. Such producers 
are commonly charged when starting 
in the morning, again at about midday 
and finally at night before shutting 
down. 

(b) With large producers it is gener- 
ally found best to charge at shorter 
intervals because more uniform results 
are thus obtained and because the fuel 
column is more easily handled when this is done. Where frequent 
charging is necessary a mechanical device such as is shown in Fig. 
397 has many advantages, the most prominent of which are: — 

(i) Uniform rate of charging so that there are no sudden 
fluctuations in quality of gas as happens when large quantities 
of green fuel are charged at long intervals; 

(2) Uniform distribution of fuel over the entire diameter of 
producer, — a very difficult matter in hand charging of large 
producers unless much hand leveling is done, which generally 
permits the admission of considerable quantities of air or the 
discharge of large volumes of gas during the operation; and 

(3) Saving of labor and hence of operating expense. 



Fig- 397- 



293. Cleaning Apparatus, (a) The gas leaving a producer 
has a comparatively high temperature and carries in suspension 



6l6 HEAT-POWER ENGINEERING 

more or less solid matter and also vapors which, upon cooling, 
will condense to form water and tar. The function of the clean- 
ing apparatus is to cool the gases and to remove solids, water 
and tar. 

(b) In the broad sense every part of the apparatus beyond 
the producer outlet flange is cooling and cleaning apparatus, but 
commercially the term is applied to the several distinct units 
such as wet and dry scrubbers, tar extractors and such. 

(c) The methods employed for cooling are almost obvious from 
the figures of actual producers shown. A certain amount of 
sensible heat is removed from the gas by air or water, or both, 
in the economizer or its equivalent. Part of the sensible heat 
of the gas is lost by radiation from the pipes connecting the 
various parts. By far the largest amount is generally removed 
in wet scrubbers, by bubbling the gas through water, or by passing 
it through a space filled with a very fine spray of water, or over 
water films on coke or on similar solid material, or by a combina- 
tion of these methods. 

(d) The methods of removing solids (and in some cases liquids) 
depend upon three principles: (i) Separation by gravitation, 
(2) separation by change of direction, and (3) separation by 
wetting solid particles and retention of such wetted material. 

Settling of solid (and liquid) matter will result to a certain 
extent when the velocity of flow is sufficiently reduced. This 
reduction in flow may be brought about either by an enlarge- 
ment in the size of the passage or by decrease in volume due to 
lowering the temperature of the gas, or by both these processes. 
In fact more or less separation of the kind always occurs in the 
pipes because of natural cooling. Separation by change in direc- 
tion occurs whenever the gas passes through an elbow or similar 
fitting, the solids (and liquids) having a tendency to travel to 
the outside of the curve. 

Special apparatus for utilizing these first two principles is 
seldom fitted to producers, and particularly not to those used 
for power work, though the fact that such separation must 
always occur to a certain extent as the gas flows through the 
passages may be utilized in design to lighten the work required 
of the following apparatus. It should also be taken into account 
in designing the piping by arranging openings through which 
cleaning can be easily effected. 



GAS PRODUCERS AND PRODUCER GAS 617 

By far the largest amount of solid material is removed by wet 
scrubbing which is also used for the cooling effect. The appa- 
ratus is so constructed that the solid particles are well wetted 
and are then allowed to separate out by gravity, or they are 
"scrubbed" out by bringing them in contact with wetted surfaces 
to which they adhere. Separation by gravity is well shown in the 
cases where gas is bubbled through water, the particles of dust 
on the surface of the "bubble " being wetted and caught by the 
liquid, after which they slowly settle to form a sort of mud. 

Separation by wet scrubbing is well illustrated by the opera- 
tion of coke or grid filled towers or "scrubbers " such as those 
shown in Figs. 391 and 392. 

Even the best wet scrubbers will allow a small amount of 
dust to pass through them. This material, together with me- 
chanically entrained water and some tar, is often finally sepa- 
rated in a "dry scrubber " filled with excelsior or sawdust, such 
as that shown in Fig. 392. 

After the tar-forming vapors have been condensed, the small 
particles or " droplets " of tar behave in much the same way as 
do the dust particles. The apparatus used for dust removal, 
and in particular the wet scrubber, removes large proportions of 
tar as well. 

(e) When the tar content of the gas is great, as when bitu- 
minous coals are used in a producer which does not provide for 
breaking up the hydrocarbons within the fuel bed, it is often 
necessary to use a separate " tar remover." These are generally 
mechanically operated scrubbing devices in which the gas is 
well wetted by a spray of water and then brought into forcible 
contact with moving and stationary surfaces. The tar collects 
upon these surfaces and the liquid is driven off or drained off 
continuously. Such separators often take forms resembling fan 
blowers, or series of propellers or impeller wheels, with adjacent 
units rotating in opposite directions. 

294. Producer Gas from Oil. (a) Many attempts have been 
made to construct producer-gas plants which would successfully 
gasify crude oil and fuel oil, but most have resulted in failure. 
There are, however, a few plants, of several different types, in 
successful operation, which indicates that the problem of gasi- 
fying oil in a producer is not impossible of solution. 



6l8 HEAT-POWER ENGINEERING 

(b) The difficulties met in attempts to gasify oil are similar to 
those experienced with the gasification of the volatiles in bitu- 
minous coals and similar fuels. Either tar, or lampblack, is 
generally produced in large quantity, and gives trouble in clean- 
ing, besides reducing the efficiency. 

(c) One of the solutions of this problem is notable for its sim- 
plicity. The producer is arranged for down draft and is built 
with a brick arch grate similar to that shown in Fig. 392. A 
bed of incandescent coke is maintained on this arch and the oil 
is sprayed into the upper part of the producer, the resulting gas 
passing downward through the coke bed. All tar-forming vapors 
are destroyed by cracking and the resultant lampblack is nearly 
all caught in the coke bed which is thus automatically replenished. 



CHAPTER XXXIV. 
UTILIZATION OF WASTE HEAT — FINANCIAL CONSIDERATIONS. 

295. General, (a) It has been seen that in connection with 
steam power plants very large amounts of heat are wasted in 
the flue gas (loss c in Fig. 3) and in the exhaust steam (width E 
in Fig. 3). The profitable reduction of these losses is obviously 
of the greatest importance, and it is the object of this chapter 
to outline briefly the different methods of its accomplishment 
and some of the more important problems connected therewith. 
In most cases it will be seen that some of the waste heat is used 
in increasing the temperature (sensible heat) of the feed water, 
thus reducing the amount of fuel required to convert the feed 
water into steam. 

296. Utilization of the Heat in the Flue Gases, (a) One very 
common method of saving some of the heat that would ordina- 
rily be wasted up the stack is to heat feed water by passing it 
through tubes which are surrounded by the flue gases after they 
have left the boiler. The heating apparatus in this case is 
commonly called an ''Economizer.'" Its use effects a saving of 
heat which in exceptional cases may amount to as much as 15 
per cent of the total calorific value of the fuel. The apparatus, 
its method of operation, advantages and disadvantages, etc., 
will be discussed in detail later. 

(b) In certain instances, some of the heat of the flue gas can 
be used profitably for heating the air used in the furnace; and 
if the local conditions are favorable, the hot gases may be used 
in drying-kilns and such. 

But in all cases where the temperature of the flue gas is de- 
creased there is a detrimental effect on the draft (if natural), 
to offset which entails an additional expense for an increased 
height of stack, or for artificial draft apparatus and its opera- 
tion. 

619 



620 HEAT-POWER ENGINEERING 

297. Utilization of the Heat in the Exhaust Steam, (a) It 

has been seen that lowering the pressure of the exhaust steam 
issuing from a prime mover results in an increase of the available 
percentage of the total heat furnished by thie boiler and hence 
reduces the proportion wasted in the exhaust. This decrease of 
pressure is commonly effected by using a condenser, of which 
there are many types. But there is in each power plant a limit 
of vacuum beyond which it does not pay to go ; and even where 
the best vacuums are used, the exhaust steam still contains the 
larger part of the heat that is brought from the boiler, and this 
heat is nearly all surrendered to the condensing water. How- 
ever, some of this heat may be returned to the boiler with the 
feed water (this being saved) but the proportion is generally 
quite small if the vacuum is good. In Fig. 3 this return is shown 
by the lower stream line, for one particular arrangement of 
plant. Condensers and methods of supplying the feed water 
with heat from the exhaust steam will be discussed more in 
detail later. 

(b) When the steam is exhausted at atmospheric pressure, 
the feed water can be heated nearly to 212° by it and thus quite 
a considerable saving may be accomplished; but only a small 
percentage of the total exhaust steam of the entire plant can be 
profitably utilized in this manner. Frequently the main prime 
mover is operated condensing and the auxiliary apparatus non- 
condensing, the exhaust steam of the latter being used for feed- 
water heating. This results, in most instances, in more profit 
than arises from operating the auxiliaries condensing. The pieces 
of apparatus in which the feed water is heated by the exhaust 
steam are called feed-water heaters; they will be discussed in de- 
tail later. 

(c) When the local conditions are suitable, some of the heat 
of the exhaust steam can be used in industrial processes which 
require temperatures lower than that corresponding to the ex- 
haust pressure. Thus, for example, a steam prime mover might 
furnish power for an industry in which the heat of the exhaust 
steam could be utilized in dryers, or in kettles used for digesting 
various materials, and the condensate, with its sensible heat, 
might be returned as feed water to the boiler. In other indus- 
tries in which solutions, having temperatures of vaporization 
below 212°, are evaporated in "evaporating pans " at atmospheric 



UTILIZATION OF WASTE HEAT 62 1 

pressure, or in ''vacuum pans " under partial vacuums, the latent 
heat of the exhaust steam can be used to supply the heat neces- 
sary to evaporate the water from the solution; and in such 
cases not only may the vacuum pan act as a condenser for the 
power plant and thus reduce the back pressure on the prime 
mover, but the hot condensate may be returned as boiler feed. 

(d) Many plants are situated in localities where the artificial 
heating of buildings is necessary for a large portion of the year. 
For such heating, low-pressure steam, i.e., steam at or near 
atmospheric pressure, is satisfactory; hence, the exhaust steam 
from engines suitably located can often be used for heating pur- 
poses for many months in each year. 

As in the case of vacuum pans, the heating system can some- 
times act as a condenser for the power plant, but in such cases 
the vacuum carried (if any) is very imperfect, the pressure not 
being much below atmospheric. Such ''vacuum systems " are 
generally operated at a pressure of but i or 2 pounds below 
atmospheric, despite the fact that the lower the pressure of 
condensation, the greater is the latent heat surrendered by the 
steam. The reasons for not using greater vacuums are: (i) 
Lowering the temperature of the steam in the radiator neces- 
sitates a greater amount of radiating surface (which involves 
greater first cost), and (2) lowering the pressure makes it more 
difficult to keep the joints tight (that is, to prevent the inflow of 
air), for even if the heating system is of only moderate extent, 
there are hundreds of joints and it is difficult to insure perma- 
nent tightness in all of them. 

In other heating systems, called Pressure Systems, the steam 
is at a pressure somewhat above atmospheric, the back pressure 
on the engine being generally from 5 to 20 pounds gauge pres- 
sure. 

(e) Supposing that the condensate from the heating system 
is used for feed water (without loss of temperature) and that all 
the heat in the exhaust steam above feed-water temperature 
can be used for heating purposes, then, in the ideal case, the 
efficiency of the combined system is 100 per cent, for all of the 
heat which is given to the steam by the boiler and not converted 
into useful work is utilized in heating. In the actual case some 
of the heat is lost by cylinder radiation, by mechanical friction 
of engine and driving machinery, and by useless radiation in_ 



622 HEAT-POWER ENGINEERING 

pipes between engine and heating system; but even then the 
efificiency of the combination is relatively high while it is in 
operation. In fact, the cylinder radiation and dissipation of 
heat due to friction and work may not be waste if the same 
amount of heat would otherwise have to be used for warming 
the engine room. 

Whether or not it would pay financially to utilize the exhaust 
steam for heating buildings depends on the location of the power 
plant, the length of the annual period of time during which the 
heating is necessary, the percentage of the total steam that can 
be used during such periods, the excess cost of equipment over 
that otherwise required and many other items which need not 
be considered in this brief discussion. 

298. Heat Transmission. — In order to transfer the heat from 
the hot gases, or steam, to the feed water or other absorbing 
media, some kind of heat transmission must occur. Hence to 
properly understand the operation of condensers, economizers, 
feed-water heaters and similar apparatus, one must have a 
knowledge of the general theory of the transmission of heat. 
The subject will, therefore, be discussed (in the next chapter) 
before such apparatus is considered in detail. 

299. Financial Considerations, (a) Suppose the installation 
of certain apparatus would effect a substantial saving in the 
weight of coal used ; then from the standpoint of heat utilization 
there would be a gain. But suppose, further, that the expense 
chargeable against the installation and the operation of the 
apparatus itself would be more than the saving in the cost of 
coal; then, of course, the installation would not be profitable 
financially. 

Obviously the advisability of the adoption of additional equip- 
ment depends on whether it will effect, in the long run, a saving 
greater than all expenses in any way chargeable against it. 

(b) The capital invested in apparatus must be guarded against 
fall in value in order to protect the investor; but the apparatus 
is subject to decrease in value because of wear and possible acci- 
dents, and also because it may become obsolete by the introduc- 
tion of improvements. This decrease in value is called "depre- 
£iation." Therefore, each year there must be set aside a certain 



FINANCIAL CONSIDERATIONS 623 

sum (a) so that the amount thus accumulated plus the remaining 
market value of the apparatus will at least equal the investment. 
The more rapidly the apparatus deteriorates or becomes obso- 
lete the greater is the annual depreciation to be set aside. 

Furthermore, the capital must receive yearly interest (b) to 
be profitable; and as the investment increases so also do the 
expenditures for taxes (c), and insurance (d); and should addi- 
tional space be demanded by the apparatus, there may be in- 
creased annual rent (e) to pay. These items, and perhaps some 
others, constitute what are called the Fixed Charges against the 
apparatus. 

(c) Besides these items, the yearly cost of operating the appa- 
ratus must be considered, the principal items of such additional 
expense being some or all of the following: — ^ (i) Labor or 
attendance; (2) fuel consumption; (3) water used; (4) oil, waste 
and other supplies; (5) repairs and maintenance, and possibly 
other items. 

' If the saving in expenditure for fuel per year should be greater 
than the sum of items {a) to (e) and of (i) to (5) and of any 
others not included, the installation of the apparatus will be a 
source of profit, otherwise not. 

(d) It is not within the scope of this book to enter into the de- 
tailed discussion of the financial problems connected with power- 
plant engineering; but it is deemed necessary to show that the 
heat saving is not the final criterion. The foregoing very brief 
discussion is given for that purpose and to make clear to the 
reader what is meant when such phrases as "aside from the 
financial considerations involved " are used in the chapters which 
follow, 



CHAPTER XXXV. 

HEAT TRANSFER. 

300. General, (a) In previous chapters it has been assumed 
possible to transfer heat from body to body at will, limited only 
by the law that a body cannot gain heat from one at a lower 
temperature unless energy is expended to cause the transfer. 
It is now necessary to investigate more closely the phenomena 
connected with the "flow " of heat under the "driving force " of 
a temperature difference. 

(b) At the outset it must be clearly understood that from the 
engineer's viewpoint the whole subject of heat transfer is in a 
most undeveloped state. Many experiments have been made, 
numerous laws have been suggested, and much that is true has 
been recorded; but there are still many points about the subject 
which are matters of dispute and the settlement of which is 
anxiously awaited. It will be shown later that this is not so 
much due to the lack of scientific knowledge as to the lack of 
means of applying known facts, and of inability to analyze the 
exact conditions under which the heat transfers occur. 

301. Heat Conduction, (a) Assume the metallic bar shown 
in Fig. 399 to be so insulated along its entire length that no heat 

can be dissipated by it to the surrounding 



I— ^ atmosphere. Assume further that the ends 



are so arranged that heat can be continu- 
ously supplied to the bar at end A and the 
p- same amount continuously removed from 

end B. Under these circumstances the heat 
supplied will all flow along the length of the bar, i.e., flow through 
the bar. Experience shows that under such conditions the tem- 
perature at B will always be lower than the temperature at A , that 
is, that there must be a temperature difference if heat is flowing. 
This is very similar to the phenomena met in the flow of electric 
currents in similar conductors. It is necessary that a difference 

624 



HEAT TRANSFER 625 

of potential exist between two points, A and B, if an electric 
current is to flow between them. In the one case then electricity 
flows "because " of a difference of electrical potential or electro- 
motive force, in the other heat flows "because " of a difference 
of temperature, or, paralleling the above, a difference of "heat 
potential." 

(b) Since it is supposed that the molecules of a substance 
move faster when at a high temperature than when at a low one, 
the sensible heat associated with the substance may therefore 
be conceived as being measured by the intensity of molecular 
motion, and heat conduction may be considered as merely the 
imparting of such motion to successive groups of molecules along 
the path of heat flow. According to this view when one end of 
a solid body is heated the molecules begin to vibrate^ more and 
more rapidly but they impart some of their energy to those 
molecules immediately adjacent to them, and these in turn pass 
on some to their neighbors, and so on through the entire sub- 
stance. 

(c) The laws governing this sort of heat flow are compara- 
tively simple. To develop them assume the two parallel planes 
A and B, in the cond'ucting body shown in 

Fig. 400, to each have unit area, to be unit 
distance apart and to be maintained at 
temperatures Ta and Tb, the former being 



one degree Fahrenheit greater than the Fig. 400. 

latter. Then there will be a flow of heat 

from A to B; and, assuming no loss from the walls of the inter- 
vening body, heat will have to be supplied at A and removed at 
B at exactly the same rate as it flows between these points, if 
these temperatures and the flow are to be maintained constant, 
(d) Experiment shows that under such conditions a very defi- 
nite amount of heat will flow from A to B per unit of time in 
any given material and this quantity is called the Specific Heat 
Conductivity. It will hereafter be designated by the Greek let- 
ter a* and, as used in most engineering calculations, it is the 
number of B.t.u. flowing per hour in the material between two 
parallel planes with area of each equal to one square foot, with 

* The letter X is very commonly used for this, but because it has already been 
employed in this book to represent another equally important quantity it is thought 
best to prevent confusion by adopting the above unusual symbol. 



626 HEAT-POWER ENGINEERING 

one inch space between and with a difference of temperature of 
one Fahrenheit degree* 

(e) It is easy to see that if planes having areas of twice this 
amount, i.e., two square feet, are assumed, twice as much heat 
would flow between them in a given time. The heat flow, or 
conductivity, therefore varies directly as the cross section, in 
the same way that electrical conductivity does. 

Similarly, to cause heat in quantity a to flow between two 
planes of unit area, but at two units distance apart, will require 
twice the temperature difference that is needed when they are 
but one unit apart. This can easily be seen by imagining an 
intermediate plane at unit distance from each of the others. One 
degree of temperature difference will cause a heat units to flow 
from plane A to the intermediate one and plane B must be one 
degree lower than the intermediate to maintain the same rate 
of flow. In other words heat conductivity, like electrical con- 
ductivity, varies inversely as the length of the conductor. 

^) A(2 = the heat flow between two parallel planes of equal 

area in a given material in one hour, 
6 = the temperature difference in Fahrenheit de- 
grees, 
S = area of each of the two planes in square feet, and 
5 = distance apart of the planes in the conductor, in 
inches, 

then, from the two statements in (e) above, 

A(> = 0.^B.t.u (428) 

o 

And, if Sa/b be called the conductivity of the heat path, its 
reciprocal b/Sa may be called the heat resistance, R, just as the 
reciprocal of electrical conductivity is called the electrical re- 
sistance. If this is done equation (428) may be written 

^Q=^^-r {b/Sa) = e/R, 

the last term of the expression resembling Ohm's Law, but giving 
the heat flowing in unit time in terms of temperature difference 
divided by heat resistance, instead of electrical flow in unit time 
in terms of voltage difference divided by electrical resistance. 

* This curious mixtiu-e of units is used as a matter of convenience in engineering 
calculations. 



HEAT TRANSFER 627 

This form of expression can be used to find heat flow with any 
compHcated combination of resistances just as is done in elec- 
trical problems, and, in general, paths with resistances in parallel 
or in series might be considered. However, in practical cases 
resistances in series are generally the only ones of importance, 
and for such instances 

A(2 = ^-^(2i?) (429) 

(g) The specific heat-conductivity, a, varies, in general, with 
the kind of conductor in about the same way as does electrical 
conductivity; thus, good conductors of electricity are generally 
good conductors of heat, and vice versa. It also varies with 
purity of material, being different for instance for pure copper 
and copper containing small quantities of other metals, and with 
temperature much as does electrical conductivity. The con- 
ductivity at at any temperature above, or below, a chosen datum 
can be expressed in terms of the conductivity a^ at datum tem- 
perature by the equation 

at = ao (i + ^t) ; 

and with 32° F. as datum this becomes 

a* = «32 1 1 + /3 (/ - 32) I , . . . . (430) 

in which jS is a constant which has values varying with the mate- 
rial, being positive with some and negative with others. 

The values of azi and jS are given in Table XXVI for some of 
the common heat conductors used by the engineer. 

Comparison of the specific conductivities tabulated will show 
that for metals they are several hundred times as great as for 
water, and that for this latter substance the conductivity is 
several times the value for gases. Stagnant gases are about the 
poorest conductors, and stagnant water is nearly as bad. 

302. Heat Transfer by Convection, (a) When fluids (liquids 
and gases) have their temperatures raised locally, the heat energy 
is distributed through the mass of fluid not only by conduction, 
such as was just considered, but also by what is known as "con- 
vection." Most liquids are comparatively poor heat conductors 
and practically all gases are very bad ones, but under proper 
conditions heat may be transferred to distant parts of the fluid 
very quickly by convection. 



628 



HEAT-POWER ENGINEERING 



TABLE XXVI.*— SPECIFIC CONDUCTIVITY OF VARIOUS 
MATERIAL^. 



Materials. 


«32t. 


^t. 




Cast iron 


330.00 


—0.0004 


Average values for gray iron. 
Variations with composition 












very great. 


Wrought iron 








(unworked) .... 


450.00 


— . 0009 


See next below as indication of 
variation. 


Wrought iron 








(worked) 


240 . 00 


—0.0006 




Steel (soft) 


300 . 00 


—0.0003 


See below as indication of vari- 
ations. 


Steel (mod. hard) . 


240 . 00 


—0.0003 




Steel (very hard) 


180 






Copper (pure) 


2400 


—0.0002 


Values given by different experi- 


Copper 

(commercial) . . . 






menters vary considerably. 


2100 


+0.0001 


1 Probably due to variations in 








purity and condition. 


Brass (yellow).. . 


420 


+0.0014 


iVaries greatly with composi- 
> tion. 


Brass (red) 


540 


+0.0008 


Aluminum (pure).. 


750 


+0.0003 




Aluminum 








with ^ °-5% Fe 
^'^^ I 0.4% Cu 


1041 


+0.0002 




Cylinder oil 


0.784 


-0.0015 


Naturally varies with kind of 
oil, cylinder oil not being a 
definite compound. 


Water 


2.6158 


+0.0053 


These values seem best authen- 








ticated. Authorities differ 








greatly. 


Air 


0. I 1989 
0-71933 


+0 . 0017 


Varies with humidity, etc. 


Hydrogen 




Fire brick 




6.948 at 1300° F. Varies con- 
siderably with composition of 














brick. 


" Insulating " 








materials 


0.4 to 1.2 




Such materials as cork, cellular 
paper, asbestos mixtures, etc. 



* Compiled largely from the Landolt-Bornstein-Myerhoffer Tabellen, and from 
"Hutte," Des Ingenieurs Taschenbuch. 

There is still considerable uncertainty and disagreement regarding the specific 
conductivities of the various substances and the U. S. Bureau of Standards is now 
carrying on investigations on this subject. The results will presumably be pub- 
lished eventually in a bulletin. 

t a; is heat in B. t. u. conducted per square foot, per degree difference, per 
hour, per inch thickness of material. /3 is the constant in Eq. (430). 



HEAT TRANSFER 629 

(b) Practically all fluids increase in volume when heated, 
that is, their density decreases. Local heating will therefore 
cause local decrease of density; but this will disturb the me- 
chanical equilibrium of the fluid and there will be a tendency for 
the heated portions to rise. This will be more marked the more 
intense and local the heating, and it results in the 
flow of the heated material through the rest, that is, 
currents are formed, or "circulation " occurs. This 
process very rapidly distributes heat energy to all parts 
of the mass even though the fluid be a poor conductor 
of heat. Examples of convection currents caused by 
local heating are shown by the arrows in Figs. 401 
and 350. 

(c) The marked distinction between heat conduction 
and heat convection can now be clearly shown, if the 
views expressed are assumed correct: Heat conduction is due 
to the individual motions of single molecules, while heat con- 
vection is the common transportation of groups of molecules. 

(d) No attempt will be made to give an expression for the 
rate at which heat is distributed through a fluid by convection, 
as it would be very complicated and of little use at best. It 
would at least involve differences of temperatures and densities, 
specific heats, viscosity and molecular friction. In general it 
may be said the heat transfer by convection will increase with 
temperature difference, or with the intensity of local heating, 
and will be greater the less the viscosity of the material. 

303. Heat Transfer by Radiation, (a) Experiment shows 
that bodies at all temperatures radiate energy at the expense of 
their associated heat, which energy, when stopped or absorbed 
by another body or medium, becomes evident as heat energy. 
This does not mean that the radiated energy is in the form of 
heat when on the way between the two bodies; in fact, if heat 
energy is to be considered as connected with the motion or con- 
dition of molecules, radiant energy of this kind cannot be heat 
as it will pass through a vacuum devoid of molecules of any kind. 

(b) Like light, radiant energy is supposed to be transmitted 
by the hypothetical "ether," and to be a vibratory form of 
energy. It is further commonly supposed that the molecules 
of a body start such vibrations in the ether at the expense of 



630 HEAT-POWER ENGINEERING 

part of their energy, and that the energy associated with mole- 
cules of other bodies can be augmented at the expense of these 
ether vibrations. Whether the ether exists or not, and whether 
the process goes on in this way or not, is really immaterial. The 
facts remain that a body can lose heat by radiating energy, 
which is not what is commonly called heat after leaving that 
body, and that substances can be raised in temperature, vapor- 
ized and so on, by receiving such radiated energy. This energy 
will hereafter be called radiant energy."^ 

(c) The rate at which heat energy is radiated by a body in- 
creases very rapidly as the absolute temperature is raised. Un- 
fortunately the exact law governing has not yet been definitely 
determined, but it seems probable that the amount of energy 
radiated varies with the fourth power of the absolute tempera- 
ture. The heat I^Qr radiated per unit of surface per unit of 
time by a body maintained at a constant absolute temperature 
T is then given by the equation 

^QR = kT\ ...... (431) 

in which ^ is a constant, which depends on the character of the 
material. 

The net loss of heat from the body by radiation is not given 
by this equation however. As any radiating body must be. sur- 
rounded by others with definite temperatures, it must be receiving 
radiant energy as well as sending it; hence, the net result of such 
an interchange would be a loss or gain of heat equal to the dif- 
ference between that sent and that received. On this basis the 
net heat lost per unit of time by unit surface of a body main- 
tained at temperature Ti (abs.), radiating to another parallel 
surface maintained at lower temperature T^ (abs.), and with 
vacuous space between the two surfaces, would be 

^QRN = kT^'-kT,'=^k{T,'-T^'). . . (432) 

which is known as Stefan's Law. 

(d) Since the radiant energy, like light, travels or radiates in 
all directions from the surface of the body which serves as its 
source, equations like those just given must be used with a certain 

* The name "radiant heat" is often given to what is here called radiant energy. 
It is not adopted in this book because of the confusion of ideas which may result 
from its use; see (i) of this section. 



HEAT TRANSFER 63 1 

amount of care. The radiating and receiving surfaces may be so 
arranged that all energy lost by one is received by the other (in 
which case Eq. (432) applies), or they may be so arranged that 
part of the energy is not caught (and Eq. (432) should then be 
modified) . 

In Fig. 402 the hot surface under consideration is supposed 
to be a small area 5 in the plane ab, which is of infinite area 
and has the same temperature throughout. ar/////////////////^/////^////////M^ 
The plane AB is a similar one of infinite — — ^'' ^ —— 



extent having a uniform but lower tem- 

. . Fig. 402. 

perature. It is obvious that the solid 

angle <^, representing the extreme angle with which the rays 

from surface 5 strike plane AB, approaches 180° as a limit, and 

that all energy radiated from S must be intercepted by AB or 

pass through it. In such case the hot surface 5' is said to "see " 

nothing but the cold surface and the radiant energy received 

from 6" by the cold surface is given in Eq. (431). 

If, however, the surfaces are arranged as in Fig. 403, in which 

the cold surface is again represented by AB, it is evident that 

Wmmm^Cm^^^^m..!^ the solid angle ^ is considerably less than 

/ \ 180 . All rays from S passmg outside of 

this angle miss the cold surface entirely and 

are lost in the space beyond. The part of 

-p. ^ the total radiant energy intercepted by the 

cold surface would then be equal to that 

given by Eq. (431) multiplied by the ratio of the solid angle 

to the solid angle 180°. Note, however, that this does not give 

the net heat lost by the hot surface, for this will be all that can 

be lost through the solid angle 180° minus all that is gained 

through that same angle. Other cases can be analyzed in similar 

manner, the amount of radiant energy received by a body 

depending on the angle (^. 

(e) The condition of the surface of a body determines to a 
considerable extent the rate at which it will give off or absorb 
radiant energy. Dull black surfaces are excellent radiators and 
absorbers. Polished metallic surfaces are very poor in both 
respects. 

(f) Some few substances are practically transparent to radiant 
energy, that is, they allow practically all of it to pass through 
their structure without absorption, but all absorb more or less. 




632 HEAT-POWER ENGINEERING 

Every substance will absorb radiant energy with the same wave 
lengths as that which it radiates, and the theoretical limit of 
transparency to radiant energy would be attained with a body 
which radiated energy of one wave length only and hence ab- 
sorbed radiant energy of that wave length only. 

Most solid substances radiate energy of many different wave 
lengths and absorb in an equally broad fashion. Gases on the 
other hand radiate energy of only one or very few wave lengths 
and are proportionately transparent to radiant energy. 

(g) In the case of two dull black, parallel surfaces of the 
same material and with vacuous space between, Eq. (432) will 
give the approximate net number of B.t.u. of radiant energy 
interchanged per hour per square foot of surface, if k has the 
value of about 16 X lo-^", the temperatures being on the Fah- 
renheit scale.* 

No real body has exactly the properties of the ideal black one, 
but sooted and lamp-blackened surfaces generally approach the 
ideal case within 5 per cent or less. 

(h) In connection with Eq. (432) it should be noted that even 
if the two radiating surfaces are so arranged that each "sees " 
only the other, kTi^ will represent all the heat lost by body i, 
but kT^^ will not necessarily represent all lost by body 2, by 
radiation in the direction toward body i ; this would be true 
only if the vibrations caused by both parallel surfaces were 
exactly alike. 

(i) In connection with the subject of heat radiation it may be 
well to call attention to an anomalous expression in common 
engineering usage. All apparatus which is maintained at a 
temperature higher than that of the surrounding atmosphere 
loses heat to the latter and this loss is commonly spoken of as 
heat lost by "radiation." As a matter of fact only part of it 
is lost in such manner, the major portion being dissipated by 
convection, and a smaller part by conduction through the 
atmosphere. 

304. Heat Transfer in Engineering Apparatus, (a) The three 
distinct methods of heat transfer so far considered are never 

* For detailed discussion of the subject see Bull. 2, U. S. Bureau of Standards, 
1905; pg. 107 of Bull. 18, U. S. Bureau of Mines; and Dalby, Heat Transmission, 
British Inst, of M. E., 1909, the latter containing references to over 500 papers 
on the general subject of heat transmission. 



HEAT TRANSFER 



633 



really found existing separately in any actual engineering prob- 
lem, for, in general, all three methods of transfer are operating 
at the same time. Nor does the engineer as a rule have to deal 
with heat transfer in or through but one substance, or from a 
single simple substance to another single simple substance. In 
general, his problems are so complicated that in the end it is 
found simpler, in the present state of knowledge, to design by 
the use of empirical or semi-empirical equations rather than to 
attempt a rational treatment of each case. 

(b) An idea of the sort of problems which occur can be given 
by considering a single case analogous to practice and developing 
the ideal equations for it, in so far as this can be done. 

Imagine, for example, a sheet of metal separating two mediums 
at different temperatures, as is shown semidiagrammatically in 
Fig. 404, in which 5 is a section through the 
metal perpendicular to its surfaces bb' and cc', 
while A and C represent sections through the 
mediums on each side of the plate. The 
dotted lines aa' and dd' represent isothermal 
planes in these mediums, the material in plane 
aa' having a temperature /i, and that in plane 
dd' having a lower temperature ^2- 

From what has already been said about con- 
duction, it is evident that heat will flow, or 
be conducted, from the plane aa' through the 
mediums A, B and C to the plane dd' so long as the tempera- 
ture difference is maintained. If the only method of heat 
transfer be assumed to be conduction, the heat flow can be cal- 
culated by Eqs. (428) and (429). 

(c) The problem of conduction may be considered to be the 
determination of the amount of heat which can be made to flow 
by the temperature difference {h — to) , through the three prisms 
with lengths 5i, 62 and 63 inches, arranged in series as shown in 
perspective in Fig. 405 (a), in which the planes aa' and dd' are 
similar to those in Fig. 404. 

(d) Investigating now in detail the assumed problem of heat 
conduction in connection with Fig. 405 (o) , it is evident that there 
must be a constant drop of temperature along the length 61, if 
heat is flowing along this first prism. This is shown graphically 
by the line from h to h at (6) in the figure, the temperatures being 




^34 



HEAT-POWER ENGINEERING 



represented by ordinates above an arbitrary chosen line which 
is not shown. The temperature drops steadily from a value h 
at the plane aa' to a value /& at the surface bb'. 

At this surface there is an abrupt and marked temperature 
drop to tb which is necessary to overcome the surface resistance 
and make the heat enter the second medium, for careful experi- 
ment shows that a surface offers a certain resistance to heat flow, 
as it is found that a temperature drop must occur at a surface 
to cause heat to enter any given mate- 
rial. This so-called surface or contact 
resistance is often compared with that 
offered by a joint in an electrical cir- 
cuit. But while there are points of 
resemblance, there are also many dif- 
ferences between the two cases, hence 
the parallel should not be carried too 
far. 

There is then a steady drop through- 
out the length 82 of the second prism 
until the temperature 4 is reached, the 
line from tb' to 4, in general, having a 
different slope from the line /i4 because 
of difference in the specific conductiv- 
ity. At the surface cc' there is again an 
abrupt drop from tc to tc' and then the 
temperature decreases through the third 
medium until the assumed temperature 
t2 is reached in the plane dd'. 
In the example illustrated in the figure, gas and water are 
the mediums on the opposite sides of the plate, as is the case 
with boiler heating surface. But in the boiler there are addi- 
tional resistances due to the soot on the external surfaces and 
scale and grease on the interior walls. 

(e) Since heat flow is equal to temperature difference divided 
by resistance, the amount of heat per hour could be found in 
this case if all the resistances were known. The resistances 
being in series they are additive, as previously indicated in 
Eq. (429), and therefore in this case 




A(2 



Ri-^R' + R2 + R" + R3 



(433) 



HEAT TRANSFER 635 

in which Ri, R2 and R3 are the resistances of the paths 5i, 82 and 
83, and R' and R" are the contact resistances of the planes bb' 
and cc' respectively. Then, remembering that unit cross section 
has been assumed, and that R = 8/Sa, this equation may be 
written 

n 

'^'3 = -!. ; — J ; — r- • • • (434) 

ai a a2 a cxs 

in which subscripts are used as in Eq. (433) and the symbols have 
the same meaning as in Eq. (428) excepting that no idea of 
length is attached to the specific heat-conductivities a' and a". 
Evidently the total conductivity per unit area is the reciprocal 
•of the denominator in Eq. (434). If this is represented by K, 
then for any area S, the equation becomes 

AQ = KSd (435) 

(f) Such equations as Eq. (434) or (435) can of course . be 
solved for any given case if the values of the specific conductivi- 
ties (a) or the total conductivity (K) are known ; but in any real 
case such a calculation would be of little value as heat transfer 
will also be produced simultaneously by radiation and convec- 
tion, the latter generally being forced to a certain extent. So 
great is the effect of convection in most engineering problems 
that it is often the most important consideration as can be well 
shown numerically. If heat is transferred from a metal plate to 
quiescent water under such conditions that convection currents 
are practically eliminated, the amount of heat transferred per 
square foot per hour per Fahrenheit degree difTerence of tem- 
perature will be of the order 2.8 B.t.u. (= at). If on the other 
hand the water be in violent motion, or in ebullition so as to 
assist convection as much as possible, the heat transferred may 
be of the order 1500 B.t.u. 

(g) It has already been seen that stagnant gases and water 
have conductivities several hundred times poorer than metals. 
Hence the stagnant film of fluid that adheres to the surfaces of 
the metal plates increases greatly the difhculty of heat trans- 
mission to and from such plates. These surface films may be 
regarded as being constituted of the molecules of fluid caught 
in the microscopic irregularities of the plate's surface, or of those 
which they entangle or retard. They act as heat insulators 



636 HEAT-POWER ENGINEERING 

which prevent the hotter particles of one fluid, and the colder 
particles of the other, from coming in contact with the plate. 
Obviously violent agitation of the fluids tends to destroy or re- 
duce the thickness of the films and thus makes the conditions 
more favorable for heat transmission. Therefore the more vio- 
lent the circulation or convection currents (within reason) the 
more rapid will be the heat transfer per square foot of surface; 
and this is not only because of the effect on the film, but also 
because the hotter portions of the fluid are brought to the plate 
at a more rapid rate. If gas and water are the two fluids, as in 
the steam boiler, the temperature drop A^i (in Fig. 405 (b)) neces- 
sary to pass the heat through the gas film is relatively very much 
greater than the drop A/2 through the metal of the plate and 
through the water film; in some cases it may represent 98 per 
cent of the difference between the temperatures of the hot gas 
and the water. 

The important part played by such films can be shown by 
an example: If a bunsen flame is placed below a metallic vessel 
containing boiling water the flame will not quite touch the metal 
but will spread out into a sheet at a distance of about ^V to 4V of 
an inch from the plate. Because of its high conductivity the 
plate on the gas side can be only a few degrees higher in temper- 
ature than the water, hence through the very short distance of ^V 
to 4^^ of an inch there must be a drop of temperature from that 
of a bunsen flame to a value only slightly above that of water 
boiling at atmospheric pressure. 

(h) Some of the difificulties which arise in actual engineering 
problems involving the transmission of heat, and the reason for 
using empirical or semi-empirical formulas, will now be apparent. 
These problems are still further complicated by the coatings of 
scale, grease, soot, paint and other material on the surfaces of the 
transmission plates and by the relative directions of the flow of 
the fluids on the opposite sides of the plates. The effect of this 
flow can be analyzed quite accurately, as will be seen in the suc- 
ceeding sections. It will first be discussed in a general way and 
later the mathematical treatment will be given in more detail. 

305. Effectiveness of Heat Transmitting Surfaces, (a) It 

has been seen that the rate of transmission of heat through a 
plate depends directly on the difference between the tempera- 




HEAT TRANSFER 637 

tures of its two surfaces. Obviously when the temperatures of 
the fluids on either side of the plate are maintained constant, 
the temperature drop is the same at all points over the surface, 
hence the rate of transmission and effectiveness of surfaces is 
uniform over the whole area. But when there is flow of one or 
both of the fluids, the conditions are quite different. 

(b) Imagine, for instance, that the tube in Fig. 406 is sur- 
rounded with boiling water (temperature constant) and that hot 
gas flows from atob, becoming cooler as it 
progresses. Then the average tempera- 
ture drop (difference of temperature) (dm^) 
through the wall back of surface Si is 
greater than that {dmj at surface ^'2, and 
this latter is greater than that (^^3) at sur- 
face 53 and so on through the length of the 
tube. With a tube of infinite length the gas could theoretically 
"be cooled to the temperature of the water and the temperature 
difference at the end b would be zero. Thus dm^ >Qm^>dm^> ■ ■ ■ 6„i„ 
and each portion of the surface is less effective than those pre- 
ceding and more so than those following. The nearer the tem- 
perature of the gas approaches that of the water the less effective 
is the adjacent heating surface, although it costs as much per 
square foot as the more effective portions. Hence, as was seen 
in Sect. 261(c), there is in each case some particular extent of 
surface which will give the greatest financial return. 

Obviously as the curve of temperature change of the gases is 
not straight, the mean temperature difference for the surface 
as a whole is not one-half the sum of the initial and final differ- 
ences. Before the case can be analyzed mathematically it will 
be necessary to find the true value of the mean temperature 
difference. 

(c) Besides the foregoing case, the cold fluid may flow and the 
hot one may be at constant temperature, or both the cold and 
hot fluids may be flowing and the currents may be either in the 
same direction or in opposite directions. In each of these addi- 
tional cases the temperature difference varies over the surfaces, 
but the methods of variation are quite different from the case 
described in the preceding paragraph. All these cases will be 
considered in detail in later sections. 

(d) In all cases of heat transmission through plates from hot 



638 HEAT-POWER ENGINEERING 

fluids to cold ones it may be noted that, neglecting radiation 
losses, the heat surrendered by the hot fluid must equal that 
received by the cold one and must also equal that flowing 
through the intervening material; hence 

aWn (Ta - n) =AQ = CcWc {h - to), . . (436) 
in which 

AQ = heat transmitted in a unit of time. 
Ch and Cc = the specific heats of the hot and cold fluids. 
Wh and Wc = weights of the fluids flowing per unit of time. 
ta and tb = temperatures of cold fluid at ends a and b (Fig. 
406). 
Ta and Tb = temperatures of hot fluid at ends a and b (meas- 
ured on the same temperature scale as that 
used for ta and 4).* 
If the object is to have the cold fluid abstract a certain quantity 
of heat A (2 in a given time with initial temperature ta, it may be 
accomplished with large weight Wc of material leaving at low 
temperature 4, or by a small weight leaving at high tempera- 
ture, and similarly in regard to the quantity of heat supplied 
by the hot fluid. Obviously the final temperature attained 
by either fluid may be controlled by regulating the weight of 
material flowing per unit of time. 

(e) Again, in all cases of heat transmission (neglecting radia- 
tion losses), the heat given up by one medium and received by 
the other must equal the conductivity of the path multiplied by 
the area of surface transmitting heat and by the temperature 
difference, as in Eq. (435). However, in case one or both fluids 
flow, the temperature difference is not constant but, as has just 
been seen, varies from point to point, hence a mean temperature 
difference dm must be used. For all conditions, then, 

A(3 = KSdm, (437) 

in which 

AQ = heat transmitted (B.t.u. per hour) 
= heat lost by hotter medium 
= heat gained by cooler medium. 

* r is not here used to represent absolute temperature but merely that of the 
hotter medium measured on the same temperature scale as t. Its use avoids the 
employment of primes, additional subscripts, or other complications that would 
be necessary to distinguish between the temperatures of the hot and cold bodies 
if the same letter, such as t, were used for both. 



HEAT TRANSFER 639 

K = conductivity of heat path (B.t.u. per sq. ft., per hr., 

per ° F.). 
6' = total surface (sq. ft.). 
dm = mean temperature difference (° F.) 
= 6 when no flow occurs. 

(f) But before Eq. 437 can be used dm must first be deter- 
mined. As will be shown later it is given for all cases by the 
equation 6—6 

'--ii^iwm (««) 

6a = temperature difference at end a of the surface. 
6b = temperature difference at end b of the surface. 

Therefore, no matter what the conditions of flow, 

^e = ^^sli7k): («9) 

306. Cases of Heat Transmission through Plates, (a) 

There are five cases of heat transmission through plates, and 
Eqs. (436) to (440) apply to all of them. They will be described 
briefly in this section and in more detail later. 

(b) Case I. (T = const.) A hot substance at constant tem- 
perature T surrenders heat to a flowing cold substance, whose tem- 
perature t is increased. Surface condensers and feed water 
heaters are examples of this case, for in both of these heat of 
the exhaust steam (at constant temperature) T=const 

is surrendered to water which is raised in 
temperature as it flows through the appa- 
ratus. This case is shown by the curves in 
Fig. 407, in which ordinates are temperatures 
and abscissas are extent of surface. The ^ Fig^To^ 
upper curve is for the hot fluid and the lower 
for the cold one, the flow being toward the right. It will be seen 
that the final temperature of the cold body depends on the total 
length of surface, and that, as the flow progresses, the tempera- 
ture t of the cold medium gradually approaches that (7" = const.) 
of the hot fluid, and the temperature difl"erence and value of the 
surface (per square foot) becomes less. 




640 



HEAT-POWER ENGINEERING 



The efficiency of the heating surface is evidently 

Ef. = Heat transmitted -i- maximum amount absorbable 

CcWc (da - e„) _ dn - dj, 



CcWc 



(441) 




Fig. 408. 



(c) Case II. (/ = const.) A substance at constant tempera- 
ture {t) receives heat from a hotter flowing substance whose tempera- 
ture (T) decreases. An example of this is the steam boiler, in 
which the boiling water (at constant temperature t) receives 
heat from the hot gases which decrease in temperature T as 
they progress. This case is the reverse of 
Case I, and Eq. (441) applies except that 
ChWh would be substituted for CcWc. Fig. 
408 is the diagram for this case. 

(d) Case III. Parallel Flow. The term 
is understood by engineers to mean parallel 
flow in the same direction on opposite sides 
of the plate. The hot and cold substances both flow in the same 
direction, their temperatures converging nearer to equality as they 
progress, as shown in Fig. 409 in which the arrows show the 
direction of flow. 

With finite surface the heat transmitted is ChWh {Ta - Tb) 
= CcWc (tb — ta). If the object is to absorb 
heat, the maximum amount which the cold 
fluid could receive is CcWcda, and the Com- 
parative Efficiency (to be used in comparisons 
with other cases) is therefore 

CcWc {tb - ta) tb - ta 




CEfc 



CcWcda 



(442) 



Fig. 409. 



But if the object is to cool the hot fluid the maximum amount of 
heat that could be surrendered is ChWhda and in that case the 
Comparative Efficiency is 

ChWh (Ta - Tb) _Ta-Tb 



CEfn 



CnWhda 



(443) 



No matter how extensive the surface, Tx, in the figure, is the 
limit of temperature to which the hot fluid can be cooled and 
the cold one heated. The heat available for transmission is 
ChWhOa (or CcWoOa) and with infinite surface only the part 



HEAT TRANSFER 641 

ChWh {Ta - T,), or aWc (T, - ta), could be transmitted. 
Hence the maximum possible efficiency is 

Ef, = {Ta -T.)^da, (444) 

or Ef, = (r. - 4) ^9a, (445) 

which is less than that attainable in any of the other cases. It 
would therefore appear that this arrangement should always be 
avoided ; however, if only a relatively small portion of the avail- 
able temperature head da is to be utilized, parallel flow may be 
advantageously used, as under these conditions it requires less 
heating surface (and hence the initial cost is less) to produce the 
same result than is required in some other arrangements. 

(e) Case IV. Counter floiv. The hot and cold substances flow 
in opposite directions, the temperature of the former approaching 
the lowest temperature of the latter, and vice versa, as they proceed. 
This is shown in Fig. 410, in which the directions of flow are 
shown by the arrows, Ta being the initial tem- 
perature of the hot fluid and 4 being that of 
the cold one. The relation between the heat 
absorbing, or surrendering, capacities of the 
two fluids is given by the ratio of CcWc to ChWh 
and this determines whether the two curves 
diverge or converge or are parallel. With infi- 
nite surface it can be shown that the hot medium 

would be cooled to the initial temperature 4 of the cold one if 
ChWh < CcWc.; or the cold medium will be raised to the initial 
temperature Ta of the hot fluid if CcWc > ChWh] and in this ideal 
case the efficiency is unity, since all the heat possible is trans- 
mitted with the materials in question. Hence the only limit to 
the efficiency is the extent of the heating surface. But a com- 
parison of Fig. 410 with Fig. 409 will show that the mean tem- 
perature head is less with counter current flow than with parallel 
flow, hence to accomplish the same degree of heating (or cooling), 
and to obtain the same efficiency, more extensive surface (at 
greater cost) is required. Counter current apparatus is there- 
fore characterized by high possible efficiency and by economy of 
amount of heating or cooling material, as an offset for the greater 
surface necessary. 

(f) Case V. {T and t both constant.) Transmission of heat 
from a hot fluid of constant temperature (T) to a cold one which 




642 



HEAT-POWER ENGINEERING 



remains at constant temperature (t). The vacuum pan is an ex- 
ample of this case, since the latent heat of the steam (at constant 
temperature) furnishes the heat for evaporating (at constant 
temperature) the other medium. 

(g) The mathematical treatment of these five cases will now 
be discussed in the succeeding sections.* 

307. Case I. (T = Const.) A Hot Substance at Constant 
Temperature Surrenders Heat to a Cold Fluid which Flows, 
(a) Assume the conditions shown in Fig. 411 and imagine that 
Wc pounds of the cooler material 
flow over the small surface 8S in a 
given time and that as a result their 
temperature is raised an amount 
5^ ( = 86). Then, if the specific heat 
of the cooler material be Cc, the 
heat 8Q absorbed from the area 8S 
per unit of time is 

8Q = CcWM = CcWc'8d; 

but this must equal the heat trans- 
mitted through 8S in the same time, 
hence 

8Q= (T-t)K'8S = dK' 8S, 
in which T and t are average tem- 
peratures (to same scale) over 8S 

and the other symbols have the same significance as in Sect. 305. 

Equating the two values of 8Q in the two preceding equations 

gives 




CoWc 



dK ' 8S, 



from which fjj^^Ja^^' 

Integration of this gives 



lOge^ = 



KS 

CcWc 



(446) 



which, rearranged and multiplied by (da — db) becomes 
* These sections may be omitted in a briefer study. 



HEAT TRANSFER 643 

Now from Fig. 411 it is seen that (da — 6b) = (k — to) hence 

CcWc (da - db) = CcWc ik - ta) ', 

but the last member of this equation is AQ, hence the equation 
above becomes /a _ n\ 

^e = ^^i|j(^ (447) 

which, in connection with Eq. (437), shows that 

(da-e,) 



(448) 



"' logeida/d,) 

as given in Eq. (438). 

(b) For certain purposes, however, it is more convenient to 
write the value of dm in another form. From Fig. 411 it is evi- 
dent that da = (T — ta) and 9b = (T — h), substituting which in 
Eq. (448) and simplifying gives the more useful expression 

Or. = ^'~^\ (449) 

log. 



T 
Transforming Eq. (446) gives 

KS 



' [awj 



e(KS/CcWc)=,n, .... (450) 



where n is the number whose Naperian logarithm is KS/CcWc, 
as given by the Log. Tables in the Appendix. 

Hence for any extent of area S, the temperature difference at 
the end b, in terms of the known value at end a, is 

db = da-^n; (451) 

and by taking different extents of area S and solving for the cor- 
responding values of db data may be obtained for plotting curves 
which show how the temperature difference varies as the flow 
progresses, for given values of K, Cc and Wc. 

(c) The efficiency of heat transmission (neglecting losses) for 
this case was given in Eq. (441). Substituting the value of db 
from Eq. (451) gives 

^/ = ^ = ^S^"-4. ■ • • (45a) 

from which the values of the efficiencies corresponding to dif- 
ferent extents of area S can be readily computed in any given 
case, and the data thus obtained can be used for constructing a 
curve to show the variation graphically. 



644 



HEAT-POWER ENGINEERING 



308. Case II. (t == Const.) A Substance at Constant Tem- 
perature (t) Receives Heat from Another Flowing Substance 
whose Temperature Decreases. This is the case shown in 
Fig. 412 and is the reverse of Case I. 
The treatment is similar to the last 
case except that T, bT and ChWh are 
substituted for /, U and CcWc. AQ 
is given by Eq. (447) without change 
and d„, by Eq. (448). 

Since in this case da= (Ta — t) and 
6b = (Tb — t), substitution of these 
quantities in Eq. (448) gives 

Ta - n 




(453) 



loge 



n-t 

Paralleling Eq. (450) 

da/db = e iKS/CuWK) = ^^ (454) 

where n is the number whose loge is {KS/ChWn). Using this 
value of n, Eqs. (451) and (452) can be applied to this case. 

309. Case III. Parallel Flow in the Same Direction, (a) 

This case is shown by the curves in Fig. 413. As in the previous 
cases the heat lost by the one mate- 
rial in passing any area equals that 
transmitted through the wall and 
also equals that received by the 
second material (neglecting losses). 
Therefore, for an infinitesimal area, 
bS in the figure, 

bQ = bTChWh = btCcWc . (a) 
and for the entire area 

A(2 = ATbChWh = MbCcWc, (b) 
where ATb and A 4 are the total 
charges in the temperatures of the 
hot and cold fluids. It is also evident from Fig. 413 that for 
surface bS 




and that 



bT-\-bt= (d - 6') 
ATb + db + Mb 



(c) 
(d) 



HEAT TRANSFER 645 

Equations (a) and (c) may now be used to derive two more 
which will be of value later. From (a) 

bTChWh - btCcWc = o, 

and multiplying Eq. (c) by CcWc gives 

8TCcWc + 8tCcWc = BdCcWc. 

Adding these last two equations and solving gives, for the small 
area 8S, q tj^ 

^^ = ^^CuwfvcWc ^'^ 

which will be used later. 

By analogy it is also evident that for the total area 5 



~''AcuW^+^Cm) ^^^ 



Substituting now in Eq. {h) the value of AT^ just found gives 

which will also be used later. 

(b) Returning now to fundamentals, it is evident, as in pre- 
vious cases, that 

hQ = hTChWh = Kd ' 8S. 
From which 

8T/d= (K'8S)/(CHWjd. 

Substituting for 57" its value from Eq. (e) and rearranging gives 

'aw, + aw. 



" -^-^^l CnW^aWo 
and integrating between the limits a and b yields 

^""^'Fr^^ aw.aw. ^^^ 

Multiplying both sides by (9„ — db) and rearranging gives 

^^" ~ ^'^ aWn + aw. - ^^log. {eje,) • ■ ■ ^'^ 

But from Eq. {g) it is seen that the left-hand member is A (2, 
hence, as in the other cases. 



646 HEAT-POWER ENGINEERING 

Comparison with Eq. (437) shows that 

^--\og. (eje,) (456) 

as in the other cases. 

From Eq. (h) ( CcWc+ChWH \ 

d, = da^e V c.wccwu ) (457) 

= ea-^n, (458) 

where n is the number whose loge is KS „ „^ „ ,,, — • 

This last equation makes it possible to determine db when 6a and 
5 are known. 

(c) From Fig. 413 it Is apparent that A.Tb = (Ta — T^). 
Substituting this in equation (/), putting db = da -r- w, and solv- 
ing gives / w rw \ 

And by analogy / w ^ t^ x 

'^ = '- + ''V-i){cJvf+kw} ■ ■ (460) 
Then if db = o, which occurs when S = ^ , Tb becomes equal to 
tb and equal to the limiting temperature Tx. Thus 

^■ = ^'~0'{aw?+awy ■ ■ ■ ('^^'^ 
^' = '' + ''{cMfkw} ■ ■ ■ (4*"') 

Since the maximum amount of heat that can be transmitted 

is (ra — Tx) ChWh = {Tx — ta) CcWc, the true efhciency is there- 
fore, in the ideal case, 

^ (Ta - Tb) aw, ^ (Ta - Tb) ... 

ir.ju ^^^_^^^^^^^ (Ta-Tx)' ' ' ' ^^ ^ 

^^^' = ' (Tx-ta)awr T7^. ^463) 

As given in Eqs. (443) and (442) the comparative efficiency 
(for comparison with the other cases) is 

c£/. = ^^V^' ^464) 

da 

CEf. = ^~^, (465) 

depending on whether the object is to cool the hot fluid or to 
heat the cold one. 



HEAT TRANSFER 



647 



310. Case IV. Counter Flow, (a) This case is shown in 
Fig. 414, the directions in which the temperature curves are 
generated being shown by the arrows. Compared with the 

other cases it is a Httle more difficult 

to develop usable equations for this ^ j^T^^^^.^^lr:^g!=i^3=! ,, 
sort of flow because, in general, only ^^^^^SS 
the initial temperatures Ta and 4 at 
opposite ends of the plate are known 
and both 9a and db are unknown. ^ 

(b) As in previous cases, however, 

8Q = 8TChWh = Kd • dS . (a) 

= 8tCcWe (b) 

Hence 

Lt.Wj, 



8t/8T = 1^ = Z, 




the symbol Z being introduced as 

this ratio will be frequently used in 

the following development. From the figure it is seen that the 

change in temperature difference over any elementary area 8S is 

86 = di - do = 8T - 8t. 

Substituting for 5/ in terms oi 8T from Eq. (c) and solving gives 

8T = 8d/{i - Z) {d) 

If this is substituted in Eq. (a) there results, after transforma- 
tion, ,, ^ _y 

K'8S, 



e CkWh 

which, being integrated between limits a and b, gives 

I - Z 



\oi 



awr 



KS, 



which, after both sides are multiplied by {da — 
gives 

(da- 



ChWu KS (da 



. . . (466) 

and rearranged, 
. . . (467) 



I - Z \0ge ida/db) ' ■ * 

(c) From the figure it is further apparent that 

An + ^6 = Ata + da] 

and from Eq. (c), by analogy 

Ata = ZAn (e) 



648 ' HEAT-POWER ENGINEERING 

substituting from which in the last equation and solving gives 

An = {da-e,)^ (I -Z) (/) 

Now A(2 = l^ThChWh and substituting the value of AT^ just 
found gives r tj/ 

A0=(«.-«^^. (g) 

(d) Returning now to Eq. (467) and comparing with Eq. (g), 
it is obvious that the left-hand member is equal to A (2, hence 

^^-Tog.(e.M) (*'^»> 

and ft — ft 

"'-i^wk) ('*^'> 

These expressions are evidently the same as in the other cases. 
However they are not of value until da and 6b have been deter- 
mined, either by the methods which will now be given, or from 
actual experiment with existing apparatus. 

(e) From Eq. (466) it is evident that 

Oa/db = e C'ftTF* = „^ (470) 

in which n is the number whose Nap. log is KS. Sub- 

ChVYh 

stituting the value of 6b from this equation in Eq. (/) gives 

. An = e.(i-^)-(i -z) (h) 

From Fig. 414 it can be seen that 

A4 = (Ta -tb- 6a), 

substituting which in Eq. (e) and solving gives 

An = (r„-4-^.)/z (i) 

Now subtracting Eq. (i) from Eq. (h) and solving gives 



\- tb . I J. I n\ 

z ' \z^ I -zr 



T 

by which the temperature difference at one end can be deter- 
mined in terms of known quantities. 



HEAT TRANSFER 



649 



(f) With da known, the value of ^6 follows from Eq. (470) ; AQ 
and dm can be determined from Eqs. (468) and (469) ; and the 
final temperatures of cold and hot fluids are 

ta= (Ta-da) (472) 

and Tb= (tb-hdb) (473) 

(g) It is important to note that the expressions in (f) can be 
used only to determine the conditions at the ends a and b or over 




the entire length of area 5. They cannot be used for interme- 
diate points, that is, for plotting the curves TaTb or tJb and the 
like. 

311. Case V. (T = const. & t = const.) A Hot Substance 
Surrenders Heat at Constant Temperature to a Cold Substance 
whose Temperature is Constant, (a) This case is exemplified 
in vacuum pans in which steam at constant temperature (T) 
surrenders some of its latent heat to evaporate a solution at 
constant temperature (t). The type of apparatus which is 
known as a "single effect vacuum pan" is illustrated in Fig. 415 
in one of its many forms and arrangements. 

(b) In such case dm = (T — t) and the heat transmitted 
through the heating surfaces is AQ = KSdm from Eq. (437). 



650 



HEAT-POWER ENGINEERING 



Neglecting losses, the weight of steam condensed in unit time 
by an amount of heat equal to A (2 is obviously 

WH = AQ/r, (474) 

where r is the latent heat of steam at temperature J" °F.; and 
the weight of solution evaporated in unit time is 

Wo = AQ/[K ~ (to ~ 32)], .... (475) 
where \c is the total heat (above 32°) per pound of the vapor 
formed at temperature t from the solution, and to is the tem- 
perature at which the solution enters the vacuum pan. 

(c) The vapor (at temperature ti) from the solution in one 
vacuum pan may be used, as in Fig. 416, to vaporize (at lower 




Fig. 416. 



temperature ^2) the solution in a second vacuum pan, the latter 
acting as condenser for the first element; the vapor from the 
second pan (at temperature ^2) may be similarly used to evapo- 
rate (at lower temperature h) the solution in a third pan, and 
so on, the vapor from the last pan being carried to a condenser. 
When more than one pan is thus used the arrangement is termed 
"multiple effect." Arrangements are called "double effect," 
"triple effect," "quadruple effect," and so on according to the 
number of pans in the series. In Fig. 416 the weak solution is 
admitted at / to the first pan from which it is fed at proper rate 
through valves Vi and V2 to the other ones. The strong solu- 
tion is withdrawn from the respective pans a.t A, B and C. 



CHAPTER XXXVI. 
APPARATUS FOR HEATING FEED WATER. 

312. Object of Heating Feed Water, (a) The principal 
advantages to be derived from heating the feed water suppHed 
a boiler are: 

(i) A decrease in the amount of fuel required to generate the 
steam, hence an increase in the over-all efficiency of the plant; 

(2) less severe strains in the boiler metal, as there is less differ- 
ence of temperature between boiler shell and the fresh feed water ; 

(3) the partial deposition outside of the boiler of scale-forming 
impurities contained in the water; and (4) an increase in the 
steaming capacity of the boilers as less heat need be transmitted 
per pound of steam generated. 

(b) An idea of the saving of fuel derived from the use of hot 
boiler feed can be obtained by analyzing an average case. As- 
sume, for instance, that the water as received at the plant has 
an average temperature of 60° F. with g = 28.08 and that it 
is converted into steam at a pressure of 150 lbs. abs. (with 
X = 1 193.4), thus requiring the addition of 1 193.4 ~ 28.08 = 1164 
B.t.u. (approx.) per pound. Assuming the specific heat of 
water as unity, every 11.64 (say 12) degrees by which the tem- 
perature of the water is raised before its introduction into the 
boiler means i per cent less heat to be added in the boiler, which 
would roughly correspond to a saving of i per cent of fuel. 

Expressed as a formula, the theoretical saving, due to using 
hot feed water at temperature //' instead of cold at temperature 
tf, in a boiler generating dry saturated steam is approximately: 

per cent saving = ^^ _ ^^ X 100, . . . (476) 
in which ^^ 

gf = sensible heat of the hot feed water above 32° F. 

= (^/' - 32) approx., 
5/ = sensible heat of the cold feed water above 32° F. 

= {ti - 32) approx., 
X = total heat of steam above 32° F. at boiler pressure. 
651 



652 HEAT-POWER ENGINEERING 

If the steam is superheated in the boiler, the saving is 



per cent saving = = 



If - <ls 



CpD -\-\ — g_f 



X 100. 



(477) 



The savings in per cent resulting from different amounts of 
feed-water heating with different initial temperatures for the 
case of saturated steam are shown diagrammatically in Fig. 417. 
These are obtained by the method just given. 

(c) Inspection of these curves will show that if water at as 
low a temperature as 40° F. is raised to a temperature of 200° F., 



ICO 

















^140 

^10 








■— ifi^ 


a^^fcg^ 















_i^ 


^ 




— 


. 


1- 









—Lbi^ 






" 





■ 





. 


—121. 






— 














9f, 




" 


■ 


. 




— 






H 


~" 




— 


. 





















%■■• 


































fe 60 
40 












f 


"or Stean 


1 Piessur 


! at 175 L 


bs.Gaugi 


) 










1 









80 100 120 140 160 

Initial Temperature of Peed Water(°F.) 



Fig. 417. 



i.e., through a range of 160° F., the saving will be slightly over 
13 per cent; and a change from 60° to 180° effects a saving of 
about 10 per cent of the fuel that would otherwise be needed. 

As the boilers do not have to transmit as much heat per pound 
of steam generated from preheated feed water as from cold 
water, smaller or fewer boilers may be used for a given output, 
when other considerations permit. 

313. Feed-Water Heaters in General, (a) One method of 
heating the boiler feed water is by using for that purpose some 
of the latent heat in the exhaust steam from a steam-driven 
prime mover (as has already been explained in Section 297), the 
apparatus in which the transmission occurs being called a Feed- 
Water Heater, or an Exhaust Steam Feed-Water Heater. 



APPARATUS FOR HEATING FEED WATER 653 

(b) If w pounds of steam are utilized for heating per pound 
of raw feed water which is at temperature tf, then 

(t/ -tf) =w[\- (t/ -32)] XEf, 

in which t/ = temperature finally attained by the feed water 
and condensed steam, 
X = total heat above 32° of i lb. of steam used for 
heating, and 
Ef = efficiency of heater. 

Then the temperature of the feed water, when w lbs. of steam 
are used per pound of feed, is 

, _ tf + w(\ + 32)Ef 

if - r+iim — ' • • • • ^478) 

and to attain a temperature of //' the weight of steam required 
per pound of raw feed is 

-- '''~^-^£/. .... (479) 



IX - W - 32)] 



In the foregoing it has been assumed that the condensed steam 
is finally cooled in the heater to the temperature of the outgoing 
feed water. Any error which is thus introduced is corrected by 
the efficiency factor. 

(c) // the condensed steam is not returned to the boiler with 
the feed, this expression for w also gives the maximum propor- 
tion of the total steam generated which can be utilized for heat- 
ing an equivalent weight of feed water. For example, if feed 
water at 60° is heated to 212° F. by steam from an engine ex- 
hausting at atmospheric pressure, and if Ef = .90, the maximum 
possible weight of steam so utilized is found to be about 17 per 
cent, or about |-th of all that is available. It is, of course, de- 
sirable that the heat in the remaining portion (|) should be 
utilized in some other way as far as is possible. 

In plants in which the main units are operated condensing, the 
auxiliary engines, which generally use less than ^ of the total 
steam, are operated noncondensing and their exhaust steam is 
utilized for feed heating. This results in greater thermal effi- 
ciency of the plant as a whole than would exist if the auxiliaries 
were connected to the condenser, since all the heat of the steam 
not used for power is then theoretically returned to the boiler. 



654 HEAT-POWER ENGINEERING 

(d) When the condensed steam (at t/) is returned to the holler 
with the feed, the total weight of feed per pound of raw feed 
is (i + w), and the proportion of raw to total is i/(i + w), 
where w is the weight of steam condensed per pound of raw feed 
as given by Eq. (479). Then the steam condensed per pound 
of total feed water is 

w' = w/{i -\- w) (480) 

which is the maximum proportion of the total steam generated 
that can be utilized for feed heating in such cases. 

(e) If the heater is located in the exhaust system between the 
prime mover and the condenser, it is called a (i) Vacuum Heater, 
and the maximum temperature which the feed water can theoreti- 
cally attain is that corresponding to the vacuum. When located 
in the exhaust system of a noncondensing unit, it is termed an 
(2) Atmospheric Heater, and the theoretical temperature attain- 
able with sufficient steam is 212°. Should the heater take steam 
from the auxiliary apparatus of the power plant it may be named 
an (3) Auxiliary Heater. If the condensate from the main units 
is not used as feed and there is not enough steam from the 
auxiliary apparatus to raise the temperature to the maximum 
otherwise attainable, the vacuum and auxiliary heaters are 
sometimes arranged in series — the water first passing through 
the former, which is then called a (4) Primary Heater, and finally 
through the latter, which becomes the (5) Secondary Heater. 
When the pressure of the steam used for heating is considerably 
above atmospheric, the apparatus is a (6) Pressure Heater. 

When the arrangement is such that the feed water and 
steam intermingle in the same chamber the heater is said to 
be of the (7) Open Type; and when the two substances are 
kept separate by heat-transmitting surfaces it is of the (8) 
Closed Type. 

314. Open Heaters, (a) Heaters of this type are generally 
in the form of rectangular boxes, or circular shells, fitted with 
coarse cascading or spraying devices to break up the water as 
it passes through and thus bring it into more intimate contact 
with the steam. They usually contain a filtering bed or settling 
chamber in which the solids carried in sUvSpension or in solution 
are more or less completely removed after heating. When 
necessary, they are also fitted with oil separators in the steam 



APPARATUS FOR HEATING FEED WATER 



655 



inlet for removing the cylinder oil from the steam before it comes 
in contact with the water. This oil, if carried over to the boiler, 
would seriously reduce the transmission of heat in that apparatus 



Water lulet 




-Open Heater. 

and might even cause overheating of the metal parts subjected 
to high temperatures. Two of the great variety of heaters of 
this type are shown in Figs. 418 and 419, the water level in the 
latter being automatically regulated by a float. 



Exhaust 
Outlet 
(Vent) 




Fig. 419. — Open Heater. 

(b) The main advantages of Open Atmospheric Heaters are: 
(i) the feed water can be heated nearly to 212° F. if sufficient 
steam is available, and surplus steam can be utilized for heating 



656 HEAT-POWER ENGINEERING 

buildings and in industrial processes where conditions permit; 
(2) scale and oil do not affect the surrender of the heat; and (3) 
the hot condensed steam is returned to the boiler with the raw 
feed, but should be purified of oil (if any is brought over from 
the engine cylinder by the steam). 

The open heater may be arranged, as in Fig. 419, to include in 
its structure (a) an oil separator, which is usually located in the 
exhaust pipe at entrance to heater, (b) a filter for removing 
sediment, part of which may be precipitate brought down by 
heating, and (c) a hot well, which may also receive the returns 
(condensate) from systems for heating buildings and such. As 
the feed water is hot and at pressure near atmospheric these 
heaters should be located above the feed pump and this latter 



MiBcellaneouB Loese 




should be suitable for pumping hot water. If the raw water is 
not available under sufficient head to flow into the heater, a 
second or cold-water pump must be added. 

(c) The proportion of the total steam generated that can be 
used for heating the feed water is obtainable from Eq. (479), 
being about ^th in ordinary cases, and the saving of fuel effected 
is given by Eq. (476) or (477), the maximum being about |th. 
Fig. 420 shows in full lines the energy stream for a power plant 
having all units exhausting to atmosphere but using as much 
waste heat as is possible in a feed-water heater; and in dotted 
lines it illustrates the same case when no heater is used. In the 
first case the over-all thermal efficiency is A /B and in the second 
AjB' , the heat supplied to the prime mover being C in both 
cases. 

(d) If the main engines are condensing, and the steam from 
steam-driven auxiliary apparatus is used for feed heating, the 



APPARATUS FOR HEATING FEED WATER 



657 



Stream line is that illustrated in Fig. 421 by the heavy lines. A 
is the heat utilized, B is the heat value of the fuel used, C is 
the heat supplied to the main and auxiliary engines, and the 
ratio A/B is the over-all thermal efificiency. 



Miscellaneous Losses 




4 Water Outlet 
►Surface 

-ofE 



But if the auxiliaries are power driven, the energy being fur- 
nished by the main units, then the case is shown in the same 
figure by the dotted lines; the useful output is A (as before), 
B' is the heat value of the fuel used, and C is the heat furnished 
to the main units, its amount being 
less than C because the water rates 
of the larger units are lower than 
those for the small auxiliary engines. 
The over-all thermal efficiency in this 
case is A/B' which is less than when 
the auxiliaries are driven by steam and 
their exhaust is used for feed heating. 

315. Closed Heaters, (a) Heaters 
of this type are so arranged that the 
steam does not come in contact with 5; 



the water. They are generally con- (orOutiet)S 
structed with straight or coiled tubes 
contained in a shell of some sort, with 
proper provision being made for in- 
equalities in expansion. The water 
generally passes through the tubes or 
coils and the steam fills the envelop- 
ing space, the condensation being drained off as it collects. The 
three most common of the many possible arrangements are 
shown in Figs. 422 to 424. 




Fig. 422. — Closed Heater. 



658 



HEAT-POWER ENGINEERING 



(b) Closed heaters are comparatively difficult to clean as a 
large part of the impurities in the water is deposited on the inside 
of the tubes and forms a coating similar to boiler scale. To 
counteract this effect, the water is often forced through the 
tubes at enormously high velocity, tending to keep them clean 
by "scouring." However the power required for pumping 
places a practical limit to the velocities used and the method is 
only partly successful. If the steam contains oil, and it is not 
removed before entering the heater, the tubes will become coated 




Inlet? 
Fig. 423. Coil Heater. 



Fig. 424. — Closed Heater. 



with this material, which is of low conductivity, and the rate 
of heat transmission will be greatly impaired. 

(c) These heaters are generally placed between the feed pump 
and the boiler, hence the former deals with cold water only and 
but one pump is required (not considering reserve pumps for 
emergencies) as against two with open heaters which do not 
receive the raw water under head. The feed water is free from 
oil, but the condensate is generally wasted. Figs. 420 and 421 
apply equally well to this case except that the heater loss E 
includes the sensible heat of the condensate (measured above 
the temperature of the raw feed) unless there is more than 
enough steam to raise the feed temperature to the maximum 
possible value. The maximum temperature attainable is gen- 



APPARATUS FOR HEATING FEED WATER 



659 



Normally Closed S 
Exiiaust Steam ^ 




Fig. 425. 



erally 2 degrees or more below the steam temperature, which 
latter depends on the pressure of the steam used. 

(d) In all such cases, the auxiliary apparatus, such as heaters, 
should be so piped that when out of commission the steam can be 
exhausted to atmosphere direct, and the feed water can be 
by-passed around the heater. The piping is therefore arranged 
somewhat as in Fig. 425, 5 and 

W being the steam and water 
by-pass valves which are nor- 
mally closed. 

(e) The saving efifected by 
closed heaters can be found from 
Eqs. (476) and (477), the tem- 
perature attained by the feed 
water is given by Eq. (478), and 
the proportion of the total steam 
generated, that can be used for 
heating the raw feed, is given by 
Eq. (479). 

(f) The heat transmission falls under Case I of Sections (306) 
and (307). The mean temperature head is given by Eqs. 
(438) or (449) and the number of square feet of heating surface 
can be found from Eq. (440) when K is known. For feed-water 
heaters K varies widely with the kind of material, character of 
surface (scale, oil film, corrugations, etc.), with the velocity of 
flow of feed water and with other factors. It ranges ordinarily 
with copper, or brass, tubes from 175 with velocity of I2| feet 
per minute and single pass, to 250 with velocity of 50 ft. per min. 
and multipass; with a velocity of 150 ft. per min. through coils 
it reaches 300 B.t.u. per square foot per hour per degree differ- 
ence in temperature, while under very favorable conditions much 
higher values are attainable. 

(g) Closed heaters with copper tubes are sometimes rated in 
terms of "heater horse power," ^ square foot of surface being 
allowed per rated horse power. On this basis, if the steam 
pressure is atmospheric and ii K = 192, the 30 lbs. (approx.) of 
feed water required per so-called boiler horse power will be 
heated from 60° to 194° (134° increase) by the | square foot of 
surface — or i sq. ft. will heat about 90 lbs. of water (the amount 
required for 3 boiler h.p.) through this temperature range. 



66o 



EEAT-POWER ENGINEERING 



316. Economizers, (a) The function of the economizer is to- 
abstract a portion of the heat from the flue gases, and to dehver 
it to the feed water on its way to the boiler, thereby somewhat 
reducing the large loss c in Fig, 3. The energy stream for this 




l:-yalueof.' 



-.•-Heat'Celi.vered:- 
:-:-:-:;b>:B6il^r;:;-. 




Boiler and Furnace Losses 

Fig. 426. 

case is shown by the full lines in Fig. 426, in which the case 
without the economizer is that with dotted lines, the boiler per- 
formance being assumed to remain unchanged. For the same 
boiler-output the fuel used is in the ratio ol B to B'. 

Erlvinff Gear 




Fig. 427. — Economizer. 



(b) One form of economizer is shown in Fig. 427. The appa- 
ratus usually consists of nests of staggered, vertical, cast-iron 
tubes fitted into top and bottom headers (with metal to metal 



APPARATUS FOR HEATING FEED WATER 



66i 




Fig. 428. 



joints), each set of headers being connected together by longi- 
tudinal branch pipes having handholes which give access to the 
interior for washing out deposits. In the upper headers are 
located removable lids opposite the ends of the tubes in order 
to give access to the latter, and power-driven scrapers constantly 
move along the external surfaces of the tubes to remove the 
deposit of soot, the scrapings falling to a pit below, from which 
they are withdrawn from time to time. The water is preferably 
introduced at the end farthest from the boiler and discharged 
from the nearer end; for its direction of flow is then counter to 
that of the flue gases, thus 
•obtaining the counterflow 
of Case IV, discussed in 
Chapter XXXV. The 
setting is either of brick 
or of sheet steel lined with 
nonconducting material 
(magnesia or asbestos) ; 
the arrangement of flues 
is such (see Fig. 428) that 
the gases from the boilers can be by-passed direct to the stack 
when the economizer is out of commission, and the water can be 
delivered direct to the boiler. 

(c) In some instances the flue gases are cooled from ordinary 
stack temperature of 550° to 650° F. to as low as 240° F. and the 
water is heated to 270° or more; temperatures much higher than 
can be obtained with an atmospheric feed-water heater. But 
because the temperature of the stack gases is low and because 
of the additional resistance in the flues due to the presence 
of the economizer tubes, the natural draft must generally be 
assisted in some manner. Hence, in connection with the finan- 
cial problem involved, the cost of such draft apparatus and 
the annual expenses chargeable against it must be added to 
the charges against the economizer itself, including those for the 
space it occupies and the power required for driving the 
scrapers. As the economizer occupies a great deal of space it 
is frequently placed either above the boiler or outside of the 
building. 

(d) In addition to the four advantages accruing in all cases 
from heating feed water, as given in Section 312 (a), the econo- 



662 HEAT-POWER ENGINEERING 

mizer has (5) a great reserve of hot water near the vaporizing^ 
point, ready to meet sudden demands on the boiler; (6) its use 
may make it possible for the boiler itself to operate with higher 
efficiency, and (7) it is especially advantageous when the boilers 
are being forced, for then the flue gases are hottest and the 
stack waste is ordinarily the greatest. Owing to the higher tem- 
perature attained by the water, some scale-forming materials 
are deposited which are not precipitated in atmospheric feed 
heaters, 

(e) If the counterflow principle is used in the economizer 
the equations of Section 310 apply. A simple approximation 
can be made however by assuming the two curves in Fig. 414 to 
be straight lines, then, at the middle of the curves, 

drr. = (Ta - An/2) - {k + A/^/s) = T^ - h - h {^Ti, + A/,), (a) 

But CpGATft = wMa (b)' 

where Cp = specific heat of gas (= 0.24), 

G = weight of gas per boiler h.p.-hr., 
w = pounds of water per boiler h.p.-hr. 
Solving (b) for ATb and substituting in (a) gives 

em=Ta-h- hAta (l + w/GCp). . . . (c> 

But the heat absorbed in the economizer by the water used 
per boiler horse power \s Q = wAta, hence Eq. (437) becomes 
(per boiler h.p.) 

wAta = KSdm (d) 

Substituting the value of dm from (c) and solving gives the 
increase in the temperature of feed water as 

^t<^ = .. ^iri7^\ (approx.). . (481) 



w / w -]- GCp \ 
K^\ 2GCp /' 



In practice 5' ranges from 2j to 5 square feet per boiler horse 
power. Corresponding to gas temperatures of 300° and 600° F. 
respectively K has values of about 2I and 2>i B.t.u. per square 
foot per degree difference of temperature per hour. The weight 
of water (w) per boiler-horse-power hour is generally taken at 



APPARATUS FOR HEATING FEED WATER 663 

about 30 lbs.; and the weight of gas (G) per boiler-h.p./hr. as 
G= (1 + 11.6^) XF, 

where x = excess coefificient, 

F = weight of combustible per boiler-h.p./hr. 
= 3 to 4 lbs. 

G is ordinarily from 80 to 120 lbs. per boiler h.p./hr. 
Then the final temperature of the feed water is 

tf = tb-\- Ata, (482) 

and the final temperature of the flue gas is 

n=Ta-An, (483) 

in which An = ^; (484) 

and if w= 30, G = 80, and Cp = 0.24 

An = i.56A/„ (485) 

(f) The per cent saving effected by raising the feed temperature 
by the amount A4 may be obtained from Eqs. (476) and (477) by 
substituting Ata for the numerator. The actual saving of boiler 
and economizer taken together may be still more, since the 
boiler may have higher efficiency because of the better conditions 
of operation. 



CHAPTER XXXVI I. 
CONDENSERS AND RELATED APPARATUS. 

317. Advisability of Condensing. The principal advantages 
accruing from the use of condensers in connection with steam- 
driven prime movers are: (i) Improved thermal efficiency of the 
unit (except in the smaller sizes) ; (2) greater power from a 
given size of prime mover; and, when the condensate is used 
for feed water, there are the additional advantages of (3) the 
thermal gain from using hot feed water and (4) the freedom 
from deposits of scale in the boiler because the feed water is 
distilled. 

However, despite the apparent advantages, it is not always 
desirable to operate condensing, for financial and other reasons. 
The additional expense for the extra equipment, its installation, 
attention and upkeep, the expenditure for condensing water, for 
pumps and their operation, and the additional space required by 
the apparatus may in some cases wholly offset the advantages. It 
is generally not considered profitable to operate condensing with 
small engines, or with simple engines of the ordinary types (some 
special types, such as the unidirectional flow engine, operate 
to best advantage when condensing) ; nor should condensers 
ordinarily be used when a considerable part of the exhaust 
steam can be employed for heating or for industrial purposes. 

318. Condensers in General, (a) The two main classes into 
which all types of condensers may be divided are: (i) Direct- 
contact Condensers and (2) Surface Condensers. In the former, 
the steam and condensing water mingle in the same chamber, 
while in the latter type they are kept separated by heat-trans- 
mitting surfaces. In each class there are many different arrange- 
ments possible and some of these will be considered in detail 
later. 

(b) Theoretically, the material handled by a condenser is low- 
pressure steam; actually it is a mixture of water, water vapor 

664 



CONDENSERS AND RELATED APPARATUS 665 

and air. Part of this air comes from the boiler, being carried into 
that vessel in solution in the feed water, and part of it leaks into 
the system through the stufifing boxes surrounding the piston 
and valve rods, through the joints of pipes and of such other 
parts of the equipment as are handling the material below atmos- 
pheric pressure. Also the water used for condensing carries air 
in solution when under atmospheric conditions, and in direct-con- 
tact condensers this air is released under diminished pressure and 
is added to that which enters in the various ways just outlined. 

(c) Then, according to Dalton's law, the total pressure within 
the condenser is the combination of the pressures of the air and 
vapor, i. e., it is the sum of their partial pressures. The import- 
ance of this fact is best appreciated from an example. 

Assume the temperature within a condenser to be 115° F. 
Then if the condenser contained only water and saturated steam 
at this temperature the pressure within the enclosure would be 
2.99 inches of mercury, corresponding to a vacuum of 26.93 
inches. If, however, every pound of steam has mixed with it 
one-quarter of a pound of air, which is not at all uncommon, the 
pressure due to this air can be found as follows : 

One pound of saturated steam at a pressure of 2.99'' Hg. occu- 
pies a volume of 231.9 cu. ft. This must also be the volume 
occupied by the 0.25 lbs. of air mixed with it, and the tempera- 
ture of this air is that of the steam (115°). Then from the law 
of ideal gases, the pressure of the air in the condenser is 

^ ^^ ^ 53.34 Xjn5 + 460) ^33^,,,^^^^^^^ 

or p = 0.46 inches of mercury. 

Thus, the total pressure in the condenser will then be 2.99" 
-|- 0.46" = 3.45 in. Hg. and the vacuum will be 29.92 — 3.45 
= 26.47 in. Hg. The back pressure on the prime mover is 
slightly higher than this, as a pressure' drop must exist between 
that piece of apparatus and the condenser in order to cause the 
steam to flow through the exhaust pipe. 

With one pound of air per pound of steam, which is a possible 
condition, the pressure due to the air would be 1.84 inches of 
mercury, under the same circumstances, and the vacuum would 
only be 25.09 inches. 

The air is thus seen to have a very appreciable effect upon the 



666 HEAT-POWER ENGINEERING 

vacuum and every precaution should therefore be taken to 
prevent an excessive amount of it entering the apparatus. If 
allowed to accumulate it would gradually increase in pressure 
and destroy the vacuum. It must therefore be removed as 
rapidly as it collects. Before it can be discharged from the 
condenser, however, its pressure must be raised to that of the 
atmosphere (or slightly above) which is done by an air com- 
pressor or pump having terminal pressures sufficiently above 
atmospheric to effect a discharge. When this pump handles 
only the air it is called an "Air Pump," or "Vacuum Pump." 

In some cases where the water is discharged from the condenser 
with considerable velocity, the arrangement is such that the air 
is ejected by the water, no separate air pump being needed. 

(d) Condensers in steam-power plants practically always use 
water as the condensing medium, but any liquid or gas that 
could be obtained cheaply, in sufficient quantities and at a low 
temperature, could be used; in fact air has been so utilized in a 
number of special instances. 

It is seldom that water is available under a head sufficient to 
cause it to flow into or through a condensing apparatus. It is 
therefore generally delivered to the condenser by a "Circulating 
Pump," which may be independently driven by steam, by electric 
motor or by belt, or may be operated by links driven by the 
prime mover. These pumps generally have comparatively low 
lifts and handle large volumes, hence the centrifugal type is 
commonly used, although there are many cases where the rotary 
or the reciprocating types have the advantage and are installed. 

In apparatus in which condensing water and steam mix and 
form a vacuum, the condensing water is often forced into the 
condenser by the atmospheric pressure acting on the surface of 
the water outside, no circulating pump being used. This is very 
common practice where the suction head is not over 15 feet, 
and it is used even with greater heads in some instances. 

(e) The removal of the water from the vacuum chamber of 
the condenser may be accomplished in several ways. If the hot 
well, which receives the condensate, can be located with water 
level at least 34 feet below the condenser, the water can be 
discharged by gravity through a "Tail Pipe," or " Barometric 
Tube," whose lower end is submerged in the hot well (the 
34-foot column of water corresponding to a 30 inch column of Hg. 



CONDENSERS AND RELATED APPARATUS 667 

on the barometer). In other cases it is necessary to have pumps 
which raise the water from condenser pressure to atmospheric. 
Such pumps are called "Tail Picmps," "Hot-well pumps," etc., 
when they handle only water (and whatever air it happens to 
have entrapped). In many instances, however, the same pump 
plunger discharges both the water and the free air, in which case 
the one pump serves both as hot-well purup and as air pump, 
and is then called a " Wet Vacuum Pump " or " Wet Air Pump.'' 

(f) Each prime mover may have its independent condenser or 
there may be a central condensing equipment for a number of 
units. In the former case the exhaust piping may be made 
short, direct and with few joints; in the latter, because of the 
greater length of pipe and larger number of joints, there is more 
opportunity for air infiltration and more resistance to flow, but 
larger and more economical auxiliaries may be used. 

In order to permit of operating noncondensing when the con- 
densing apparatus is out of commission, the exhaust pipe should 
contain a valve which can be opened to the atmosphere. This 
valve is usually arranged to open automatically when the con- 
denser ceases to operate. To permit of repairs while the engine 
is running there should be a shut-off valve in the exhaust pipe 
leading to the condenser; and should several condensers dis- 
charge to a common main there should also be shut-off valves 
between them and that pipe. 

319. Contact Condensers, (a) There are several different 
kinds of contact condensers only a few of which will be described. 
That in Fig. 429 is known as the "Ordinary Jet Condenser.'' * 
In it the injection water entering at / and the steam entering at S 
mingle in the conical condenser head B and the resulting mixture 
of condensate, injection water and noncondensable gases is raised 
to atmospheric pressure and discharged by the wet air pump 
located below, the flow of injection water being regulated by 
handwheel H. At (a) in Fig. 429 is a diagram of the piping for 
such a condenser. It includes an atmospheric relief valve {A) 
which will automatically open to the atmosphere when the valve 
V is closed for making repairs to the condenser, or when the 
vacuum is "broken," as when the injection water fails. 

* The term "Jet Condenser" is also used as being synonymous with "direct 
contact condenser." 



668 



HEAT-POWER ENGINEERING 



If the suction lift for the injection water is not too great this 
water may be siphoned into the condenser by the vacuum after 
it has been estabHshed by priming and starting the pump. In 
such cases this hft may be as much as 15 to 18 feet, provided the 
piping is short and not restricted. When the water is suppHed 
in this manner there is danger of flooding and wrecking the 
engine in case the pump ceases to operate before valve C is closed, 
or if it runs so slowly that it cannot discharge the water as fast 
as it collects. To prevent the possibility of such disaster various 




Fig. 429. — Jet Condenser. 



expedients are adopted, such as providing a float (F in Fig. 429) 
which, when the water level becomes dangerously high, will be 
raised and open a valve v to admit the atmosphere to the con- 
denser and thus "break " the vacuum and stop the flow of 
injection water. 

If a pump is used for the injection water the head against which 
it operates is the difference between the total head and that 
through which the water would be "drawn " by the vacuum. 



CONDENSERS AND RELATED APPARATUS 



669 



(b) The term ''Barometric Condenser " may be applied to any 
form of direct-contact condenser having the barometric tube. 
Fig. 430 shows one arrangement commonly called the " Siphon " 
Type* The injection water entering the condenser head B 
from pipe / passes downward in a thin annular sheet around the 
hollow cone in the condenser head and unites with the steam 
which passes through the cone. The mixture is discharged 
through the neck or throat N with sufficient velocity to carry 
with it the noncondensable gases. A is an atmospheric relief 
valve and iJ is a handwheel for regulating the injection water. 
The water level L in the tail ^^ 
pipe depends on the vacuum tlTir/v!"! Ew. ==^h Regulator 
maintained, but for safety the tail 
pipe is extended 34 feet above 
the water level in the hot well. 

If injection water is available 
at a head h (in the figure) of not 
over 18 feet, it may be "drawn 
in " by the vacuum after this has 
once been established by opening 
the lower valve shown dotted, or 
in some other manner, and in 
such case, the pump P can be 
dispensed with. At the foot of r~f- 
the exhaust pipe there should be 1—^ 
eitheradrain,or an "en trainer," 
the latter being so arranged that 
the exhaust steam impinges on 
the surface of the water which 
has collected in a pocket, and 
gradually picks it up in small 
particles and disposes of it by 
entrainment. Because of the 
great head room required by these condensers they are fre- 
quently located outside of the power house; and sometimes a 
Tail Pump is substituted for the tail pipe, as in Fig. 431. 

(c) Fig. 431 shows a direct-contact condenser somewhat simi- 

* All direct-contact condensers can be used to siphon the condensing water, 
tut the term " Siphon Condenser " is generally applied only when there is the 
neck N shown in Fig. 430. 




Fig. 430. Siphon Condenser. 



670 



HEAT-POWER ENGINEERING 



lar to the one just discussed except that it uses a "dry air 
pump ' ' for removing the air. As the volume of air to be 
handled will increase with its temperature, and as the size 
of the dry air pump will increase with the volume of the 
air, the latter is usually cooled in some manner before it 
goes to the air pump. In the arrangement shown this is done 
by passing it through a spray of cold water, in the upper 
part of the condenser head, on its way to the discharge opening. 




Fig. 431. — Condenser with Dry Air Pump. 

(d) The Ejector Condenser, shown diagrammatically in Fig. 432, 
operates on the same principle as the steam ejector which is used 
for forcing water into boilers against the pressure of the steam. 
The injection water enters at / and passes through the neck of 
the combining tube B, where it rapidly condenses the exhaust 
steam which passes through small nozzles in the wall of this 
tube. Some of the heat surrendered by the condensed vapor 
is converted into kinetic energy of the steam jets flowing through 
these nozzles and the momentum acquired propels the water 



CONDENSERS AND RELATED APPARATUS 



671 



with high velocity through the neck. This velocity is reduced 
in the expanding tube below so that the pressure is raised to 
atmospheric when the end E is reached. 

To start the flow of injection water with the arrangement 
shown, boiler steam may be admitted through the starting 
valve C. This steam then issues through the check valve D 
and partly exhausts the atmosphere from the injection pipe, thus 
causing the water to rise and enter the condenser. The valve 



Starting Valve 
C 




Fig. 432. — Ejector Condenser. 

C may then be closed, the exhaust steam continuing the circu- 
lation of the water in the manner just described. The siphoning 
of injection water can also be started by admitting high pressure 
water through the starting valve C, in which case valve D can be 
omitted. 

The operation of the condenser ceases, of course, when the 
supply of exhaust steam is discontinued, hence this arrangement 
of condenser cannot be used for intermittent service, nor is it 
satisfactory if the load varies widely and frequently. With 
steady load the " suction lift " may be 16 feet; with variable loads 
it is limited to a smaller value. 



672 HEAT-POWER ENGINEERING 

The combining tube may be arranged with adjustable internal 
throttling device and external sleeve to permit the regulation of 
the water and steam openings to suit the load. Should the 
water contain foreign matter a strainer should be located in the 
injection pipe. 

If the condensing water is supplied under a head of 20 feet, or 
more, a slightly modified arrangement can be used and a more 
certain vacuum obtained even with wide variations in load. 

(e) With all types of contact condensers the weight of water 
required per pound of dry steam for any vacuum is 

-"^^^ (^-) 

where X^ = total heat above 32° F. per pound of steam at 
exhaust pressure, 
ti = temperature of injection water, ° F., 
tm = temperature of mixture, ° F. (This is generally 
from 10 to 15° less than the temperature of the 
exhaust steam), and 
Ef = efficiency of heat absorption (= 0.85 to 0.95). 

The temperature of the water in the hot well is practically 
that of the mixture, and this water is available for boiler feed 
when the character of condensing water permits. The weight 
of water to be handled by the circulating pump per hour is 
w X weight of steam condensed in that time, and the weight 
delivered by the discharge pump is (w + i) X wt. of steam. 

(f) The principal advantages of direct-contact condensers 
are: (i) Their simplicity; (2) low first cost; (3) low cost of 
upkeep; and (4) small space required. They have, however, 
certain detrimental features which in some instances may partly 
or wholly counterbalance these advantages: (a) If the in- 
jection water is sea water, or has scale-forming impurities, or is 
otherwise unsuitable for boiler feed, none of the heat in the 
condenser discharge can be returned to the boiler; (b) the dis- 
tilled water resulting from the condensation of the steam is lost 
since it is mixed with the injection water, whereas with surface 
condensers it is available for boiler feed; (c) the temperature of 
the hot-well water used for boiler feed is lower than that from a 
surface condenser of proper design; (d) it is more difficult to 
obtain a good vacuum than with surface condensers, because of 



CONDENSERS AND RELATED APPARATUS 



673 



the air introduced by the injection water; and (e) larger air 
pumps are therefore required. 

320. Surface Condensers, (a) A water-cooled surface con- 
denser is essentially an enlargement in the exhaust piping through 
which pass tubes which contain the flowing condensing water. 
If this water flows merely from one tube header to the other, the 
apparatus is called a "single pass" condenser, and "multipass 
condenser " is the general term applied when the water flows 
across the steam chamber two or more times. A double-pass 
condenser of the ordinary type is shown in Fig. 433, with cooling 



Discharge fi 




PQ 



^^B^^^^ 



rxT 



Fig. 433. — Double Flow Surface Condenser. 

water flowing from the lower part (A) of one head to the other 
head (B) and then back to the upper part (C) of the first one. 

The arrangement of piping for a surface condenser resembles 
that for the jet condenser in Fig. 429(a). In order to insure 
the flooding of all the condenser tubes at all times the condensing 
water is usually introduced at the bottom of the condenser and 
discharged at the top. 

(b) The surface condenser has certain advantages over the di- 
rect-contact type. The principal ones are as follows: If the con- 
densate is used as boiler feed, (i) substantially all of the available 



674 HEAT-POWER ENGINEERING 

sensible heat of the exhaust steam is returned to the boiler; 
(2) the same water is used repeatedly, thus avoiding the ex- 
pense for new water (which is of importance only when suitable 
water is difficult to obtain or when its cost is high) ; (3) the 
feed water is distilled and free from scale-forming impurities; 
(4) less air is carried into the boiler by the feed water; and (5) 
sea water or any other water which is unsuitable for boiler feed 
can be used for cooling and yet the available sensible heat of the 
exhaust steam is returnable to the boiler; (6) better vacuums 
are generally obtainable with smaller air pumps and less power 
for same, because of (4) and because the air entrained in the 
condensing water is kept separated from the steam: and (7) 
there is no possibility of the circulating water flooding and wreck- 
ing the prime mover. 

The principal disadvantages are the relatively large (a) first 
cost, (b) space occupied, (c) upkeep expense (the latter being 
largely due to the corrosion and deterioration of condenser tubes 
and to the multitudinous joints which must be maintained free 
from leakage), and (d), in the case of steam engines, the presence 
of oil in the condensate. The latter item does not hold with 
turbines. The surface condenser requires at least two pumps 
(the wet air and the circulating water pumps) and may use a 
third (a separate dry air pump) when the best results are desired. 
In contrast, some direct-contact condensers have no pumps, and 
others only a wet or dry air pump. 

(c) The weight of condensing water required per pound of ex- 
haust (with quality unity) is evidently 

- = ^i^f^' • • • ■ • (^«'> 

where Xx = total heat above 32° F. per pound of exhaust steam. 
tc = temperature of the condensate leaving the condenser 

= (from o to 20° F. below the exhaust temperature 4),* 
ti = temperature of condensing water at inlet, 
td = temperature of condensing water at discharge, 

= (from 5 to 10° F. below the exhaust temperature 4). 

With from 25 to 26 inches of vacuum w is from 25 to 30 lbs. 
depending on the value of ti ; and with better vacuums w is from 
45 to 55 lbs. and even more. 

(d) The heat transmission in Surface Condensers is according 



CONDENSERS AND RELATED APPARATUS 



675 



to Case I of Seclions 306 and 307 and the amount of condensing- 
surface required to condense ic lbs. of exhaust steam per hour 
(quality unity) is from Eq. (437). 

= w\\,-{t,-2>2)\^dmK, . . . . (488) 

where the symbols in the bracket have the same meaning as in 
Eq. (487) ; and from Eq. (438) 

ern^ik-td-^ixog/f^"^ (489) 

The value of K depends on the surface coating on the tubes 
(scale and oil), on the velocity of the water, on the air present 
in the steam, on the material of the tubes (although this is 
usually negligible) and on other items. It ordinarily ranges 
from 250 to 300 B.t.u. per square foot per degree F. per hour in 
the simpler types of condensers under ordinary conditions, but 
with the best designs, well drained, and with good air pumps,, 
the rate of transmission may be from two to three times these 
values. For ordinary condensers with from 24 to 26 inches 
vacuum about 10 lbs. of steam are condensed per square foot 
of heating surface per hour. 

For small turbines with high vacuums from 2^ to 4 square feet 
of condensing surface are ordinarily used per kilowatt rating of 
the generator; and with large turbines from i to 2| sq. ft. are 
found with the best types of condensers. 

(e) The essentials which make Surface Condensers most effec- 
tive are: (i) All the tube surface should be available for heat 
transmission; none of it should be air-bound 
either on the steam or water side. (2) The 
falling condensate should not "drown " any 
tubes, for then (a) the surface is only about 
10 per cent as effective, (jb) the condensate is 
cooler, hence not so valuable as feed water, 
and (c) more condensing water is required. 
(3) The velocities of the steam and water 
should be high enough to break up the surface 
films. As the transmission's largely depend- 
ent on the heat-absorbing ability of the water, 
the more rapidly the latter is brought in contact with the tube 
surfaces, the greater the rate of transmission. (4) The air in 




Fig. 434- 



676 



HEAT-POWER ENGINEERING 



the condensate should be cooled as much as possible to decrease 
the volume to be handled by the air pump and to reduce its par- 
tial pressure acting on the prime mover. (5) There should be 
suitably arranged baffles to so distribute the steam that all parts 
of the condensing surface are equally effective. 

(f) Fig. 434 shows one form of dry-tube condenser with ar- 
rangement for preventing the lower tubes of the condenser from 




Fig- 435- 



being drowned and from serving as condensate coolers. This 
is accomplished by the baffles A, B, which are arranged to collect 
and draw off the condensate from the tubes immediately above 
as rapidly as it is formed. Baffle pans somewhat similarly 
arranged (with drains) are used in like manner in other con- 
densers of this type. 

(g) In some condensers the counter-current principle is used 



CONDENSERS AND RELATED APPARATUS 677 

as regards the condensate. In such cases the exhaust steam 
enters the condenser at the bottom, hence the falhng condensate 
passes downward through this upflowing steam and becomes 
heated thereby, the feed water then being substantially at 
exhaust temperature. 

(h) As a cubic foot of air is heavier than a like volume of 
steam at the temperatures existing in condensers, and as it is 
coolest and most dense at the bottom of the shell, it tends to 
gravitate, hence the wet air pump placed below the condenser 
is correctly located for receiving the air as well as the con- 
densate. 

(i) Fig. 435 shows the piping of a condenser having separate 
dry air and hot-well pumps. The arrangement includes an air 
cooler through which the air passes on its way to the dry air 
pump, the condensed vapor from this cooler being passed through 
a water seal to the hot well where the condensate collects. 

321. Air Pumps, (a) As has already been seen a Dry Air 
Pump is an air compressor which receives thfe air (and its en- 
trained moisture) at condenser pressure 
and compresses it sufficiently to permit 
of discharge to the atmosphere, the com- 
pressor card resembling Fig. 436 in the 

best instances. As the compression ratio j \ ^T~" =I ^m^ 

is high, the clearance volume must be 

small, for no air can be received from ' t-- ^ ' 

fig. 430. 
the condenser until that in the clearance 

space is expanded to condenser pressure. To increase the volu- 
metric efficiency the three expedients most commonly used are: 
(i) The air may be compressed in two stages; (2) an equalizing 
passage (as a in Fig. 437) may be so arranged that at the end of 
the stroke the clearance air may at the proper time be moment- 
arily exhausted into the other end of the cylinder which is filled 
with air at condenser pressure, thus when the stroke begins the 
clearance space is under pressure nearly equal to the vacuum; 
and (3) the clearance space may be filled with water, as is the 
case in wet air pumps. 

Air pumps as well as the other pumps are usually steam driven, 
as the exhaust steam can ordinarily be advantageously used for 
feed-water heating. 




678 



HEAT-POWER ENGINEERING 



(b) A Wet Air Pump of the ordinary horizontal reciprocating 
type is shown at the left in Fig. 433, 5 indicating the suction 
valves and d the discharge valves. One of the vertical types is 
illustrated in Fig. 438 with foot valves, bucket valves and dis- 
charge valves as shown. In the Edwards type, shown in Fig. 439, 
the foot and bucket valves are dispensed with, and whatever 
condensate collects in the base of the pump is displaced and 
forced into the pump cylinder by the conical end of the plunger 
as it approaches the bottom of its stroke. This water and the 
air above are then caught above the plunger when it ascends and 
are discharged in the usual manner. As in most pumps, there 
is a lip around the upper valve deck so that the valves will always 




Fig. 437. — Dry Air Pump with Equalizing Passage. 

be water sealed to prevent air leakage. Other single-acting 
vertical pumps and double-acting horizontal ones are somewhat 
similarly arranged to operate without foot and bucket valves. 

A wet air pump of the Rotary Type is shown in Fig. 440, it 
being so arranged that the water-sealed lobed wheels not only 
discharge the water but also carry along the air which is intro- 
duced at A below the wheels. 

(c) The Leblanc type of dry air pump is shown in Fig. 441. 
Water in chamber A, "drawn in " by the vacuum, is discharged 
at B and is projected downward by the vanes on the rotor R in 
a series of layers which, acting as pistons, entrap the air entering 
at C and force it through the neck N against the atmospheric 
pressure. To start the vacuum live steam may be temporarily 
admitted at S. 



CONDENSERS AND RELATED APPARATUS 



679 



(d) The volume of condensate (Vc) and that of condensing 
water ( Vw) used per minute can be readily estimated and the 
necessary size of pumps can then be determined if water alone 
is to be handled. If, however, air is to be pumped there is no 
exact method of arriving at the volume {Va) to be discharged 
per minute and the proportions of the pump are based on rough 





Fig. 438. —Wet Air Pump. 




Fig. 439. — Wet Air Pirnip, Edwards Type. 



Fig. 440. — Rotary Type of 
Air Pump. 



estim.ates. Surface water under atmospheric conditions may 
contain by volume from 2 to 5 per cent of air, and the leakages 
may increase the percentage of "atmospheric air" in the con- 
densers to from 7 to 10 per cent. Under partial pressure and 
higher temperature conditions the volume of this air is greatly 
increased and its value can be readily computed, and serves as 
a rough basis for determining the size of the pump. 



68o 



HEAT-POWER ENGINEERING 



According to Gebhardt* single-acting wet vacuum pumps for 
jet condensers ordinarily have plunger displacements per minute 
of about 3 Vw, where Vw is the volume of the injection water 
pumped in that time, and double-acting pumps have displace- 
ment 3I Vw, the piston speeds being about 50 feet per minute. 
With reciprocating engines the wet air pump for a surface con- 




Fig. 441. — Leblanc Air Pump. 

denser ordinarily has a displacement of 10 Vc, where Vc is the 
volume of condensate, and for steam turbines it is about 20 Vc, 
these values being the average of two hundred plants. For dry 
air pumps the displacement of the plunger ranges from 20 to 30 Vc 
with vacuum below 27 inches, up to 50 Vc for 28 inches and over, 
these values being based on an investigation of fifty installations. 

* Gebhardt's " Steam Power Plant Engineering," published by John Wiley 
and Sons. 



CONDENSERS AND RELATED APPARATUS 68 1 

322. Recovery of Condensing Water, (a) The amount of 
water required in a plant for condensing purposes is relatively 
very great, varying, as shown in Sec. 320(c), from about 25 to 
55 pounds per pound of steam condensed. After being used 
this water is generally wasted, hence a continuous supply of 
fresh water is required in such cases. When a plant owns its 
own water supply or is situated near a large river, or other body 
of water, from which it can pump condensing water, the cost of 
the water is practically only that of pumping. Many plants are 
so situated, however, that the only source is the city mains and 
in such cases the continuous expenditure for condensing water 
may be far in excess of the saving effected by its use. Methods 
of cooling and storing condensing water have been developed, 
therefore, so that the same water can be used repeatedly and 
thus make it possible to obtain the benefit of condensing opera- 
tion in cases where the cost of a continuous supply of fresh 
water would be prohibitive. 

(b) For cooling the water, various evaporative cooling devices 
are in use. They all operate by exposing large surface of water 
(sometimes in thin sheets or in drops) to air currents, the cooling 
being effected both by the direct contact of the cooler air with 
the hot water and by the evaporation of part of the water. For 
this purpose (i) a pond having relatively large exposed surface 
may be used ; or (2) the water may be sprayed into the air and 
allowed to fall into a pond; or, (3) it may be passed through a 
cooling tower, such as described in the following paragraphs. 

(c) Cooling towers are roughly divided into two classes: 

1. Natural draft cooling towers, and 

2. Fan towers or forced draft towers. 

In the natural draft type, a vertical, rectangular or cylindrical 
shell is filled with some material or structure (trays, slats, wire 
screens, etc.) adapted to spread the water into thin sheets or 
streams. The water is introduced at the top, gravitates over 
this filling to a reservoir in the base of the tower and is then 
returned to the condenser. 

Air enters at the bottom of the tower and passes upward 
through the filling so that cooling takes place on the counterflow 
principle. The upward motion of the air in the tower is due to 
the fact that its temperature and humidity are greater than 



682 



HEAT-POWER ENGINEERING 



those of the outside air and it is therefore constantly displaced 
upward by fresh, cool air entering at the bottom. This effect 
(the "draft") is increased by lengthening the column of hot moist 
air by the addition of a "fine," or "stack," above the filling. 

(d) A fan type of tower is essentially the same as one with 
natural draft so far as filling and cooling are concerned; the 
stack is omitted, however, and the draft is assisted by fans 




which force air in at the bottom of the tower. Such a struc- 
ture, of which there are many arrangements, is shown in Fig. 
442. This type of tower has the disadvantage of requiring an 
expenditure of power to operate the fans, but is independent of 
atmospheric conditions so far as draft is concerned. 

A combination of both types is occasionally used, the stack 
supplying draft when possible and being helped out by the fans 
when necessary. 



CONDENSERS AND RELATED APPARATUS 683 

(e) Neglecting losses, the heat abstracted in a given time 

from the exhaust steam in condensing it equals the weight of 

the condensate (w^) times the latent heat (rx) of the exhaust 

steam at its partial pressure, and this, of course, is the amount of 

heat absorbed by the cooling water. Hence, if this water is 

used repeatedly, it must first be cooled by the surrender of this 

same amount of heat before its return to the condenser. This 

cooling is accomplished principally by the evaporation of a 

portion of the water, the heat carried away in this manner being 

equal to the product of weight (w^) vaporized in the given time, 

by the latent heat (r^) at the partial pressure existing at the 

surface exposed to the atmosphere. Then, considering that the 

cooling is effected entirely by evaporation and neglecting losses, 

it follows that / \ / \ / \ 

{wr)x = iwr)^ ; (492) 

or, the weight of cooling water evaporated in a given time is 

approximately , ' , 

^^ w„ = w^r^/r^ (493) 

But, as Yx and Vv do not differ greatly, it is roughly true that 
w„ = Wx, — that is, under the conditions assumed, the weight of 
condensing water vaporized in the cooling device is about equal 
to the amount of condensate formed in the same interval of 
time in the condenser in which that water is used. Thus, if all 
the steam generated is condensed in a surface condenser and 
returned to the boiler, no new water (theoretically) is needed 
for boiler feed, but about an equal weight of make-up water 
must be constantly added to the supply of cooling water; and 
with surface condensers this water may, of course, be of quality 
unsuitable for use in the boilers. This is theoretically the maxi- 
mum amount that need be lost in the process of cooling. 

(f) If the air were so fully saturated that it could receive no 
more moisture, none of the water would vaporize and no cooling 
would be eflfected in the manner just described. In such case 
heat could still be abstracted from the water by bringing cooler 
air and its moisture in contact with it. The cooling media 
would then have their sensible heat raised by absorbing heat 
from the water, but it would take a great quantity of air to 
effect the cooling in this manner. 

(g) The actual case is intermediate between the two extremes- 
just discussed. The atmospheric air is practically never fully 



■684 HEAT-POWER ENGINEERING 

saturated but nearly always has some humidity. In the aver- 
age cooling tower from | to ^ of the heat is carried away by the 
increase in the sensible heat of the air and its vapor, and the 
rest by evaporation. The actual operation of the cooling de- 
vice is dependent on the humidity, temperature, amount and 
distribution of the air and on the temperature and extent of 
exposed surface of the water. Ordinarily, under unfavorable 
conditions, one cubic foot of air entering can be expected to 
remove at least 2^ B.t.u. as sensible heat of the air and latent 
heat of vaporized water ; from 2 to 4 per cent of the condensing 
water is all that need be lost by evaporation ; and the condensing 
water can be readily cooled 40 to 50 Fahrenheit degrees. 



CHAPTER XXXVIII. 

WATER PURIFICATION 

323. Impurities in Natural Waters, (a) Waters available for 
power plant use are never the simple H2O of chemistry but 
always carry certain impurities in suspension and in solution. 
When taken from streams or lakes the water generally has large 
quantities of mud and silt in suspension at certain periods of 
the year; in some cases at all periods. Water taken from 
sources which receive large deposits of leaves, twigs and other 
vegetable and animal remains will always carry certain organic, 
substances in solution and sometimes in suspension as well- 
Practically all waters found on, or below, the earth's surface 
contain inorganic salts and gases in solution and sometimes free 
acids as well. 

(b) All such impurities are liable to cause trouble in power 
plants, either (i) by clogging tubes and pipes, or (2) by corroding 
metal surfaces, or (3) by incrusting heat-transmitting surfaces,, 
or (4) by causing foaming within boilers and similar apparatus. 

(c) When solid material in suspension is of large size it can 
often be separated by simple mechanical means, as by screening, 
by settling, or by filtering through beds of coke, broken rock, or 
sand. When fine it can be removed by first entangling it in a 
flocculent precipitate and then filtering, as is done with municipal 
supplies. 

In general, however, after such treatment average water will 
still contain in solution quite a quantity of material which will 
cause trouble if allowed to enter the apparatus of a power plant. 
The greatest difficulty is experienced in steam boilers and in the 
jackets of internal-combustion engines because of the deposition 
of such dissolved material upon the metal surfaces, thus forming 
a crust, or a scale, which materially decreases heat conductivity, 
clogs the passages, and may lead to the overheating of metal 
plates or surfaces. Acids in solution may cause corrosion of 
such surfaces. 

68s 



686 HEAT-POWER ENGINEERING 

(d) To prevent troubles of this character water is often 
*' treated," "softened," or "purified," before use. The problem 
of water treatment is very large and by no means entirely solved 
as yet. In the following paragraphs the fundamental principles 
and the most common methods of treatment of boiler feed 
waters will be very briefly considered. 

324. Troubles from Untreated Feed Water, (a) If untreated 
water is fed to a boiler the following troubles may ensue: 

(i) Corrosion may occur because of 

(a) Free acid, such as H2SO4 and HNO3, which will not only 

attack the metal of the boiler, but if present in larger 
quantities than 5 parts per i ,000,000 * will often 
corrode or pit the metal parts of the engine with 
which the steam comes in contact; and because of 

(b) Organic material, such as infusions of leaves, sewage and 

such, which acts as though acids were formed within 
the boiler. 

(2) Incrustation may occur because of 

(a) The deposition of suspended matter, such as mud, in parts 
of the boiler in which the circulation is not sufficiently 
rapid to maintain it in suspension; 

(&) The concentration of salts brought into the boiler with 
the feed water and left behind by the issuing steam; 

if) The deposition of decomposed salts, such as the soluble 
bicarbonate of calcium, Ca{HCOz)i, which when 
heated loses one molecule of CO2 and one of H2O, 
leaving insoluble CaCO^; 

id) The deposition by heating of salts which are less soluble 
in hot water than in cold, as calcium sulphate, CaSOi, 
the solubility of which at ordinary steam tempera- 
tures is only about one-fourth as great as at ordinary 
atmospheric temperatures; and 

{e) The deposition of soaps formed by the saponification of 
greases and organic oils by alkalies present in the 
feed water. 

* Parts per, 1000, 100,000 and 1,000,000 are the terms commonly used for 
•expressing the results of water analyses. Since one U. S. gallon of water at 60 
degrees F. weighs 58,335 grains, one part per 100,000 is equal to 0.584 grain per 
U. S. gallon. 



WATER PURIFICATION 687 

(3) Foaming may be caused by 

(a) The decomposition or modification of salts to form floc- 

culent precipitates which collect as a scum on and 
near the surface of the water; and by 

(b) Organic matter, grease, soaps and such, which form 

similar scums. 

(b) By far the most troublesome salts commonly found in 
feed waters are those of calcium and magnesium. They are 
generally either the carbonates or the sulphates of these metals. 
The carbonates of calcium form a more or less granular scale 
which it is not very difhcult to remove with the tools used for 
cleaning boilers. The sulphate of calcium forms a very hard, 
porcelain-like scale which is removed only with great difficulty. 
Magnesium carbonate generally gives rise to a scum, causing 
priming, and also forms a hydrate which serves to cement to- 
gether other scale-forming materials. The sulphate of this metal 
decomposes at high temperatures, liberating sulphuric acid which 
may cause corrosion and forming the hydrate which acts as a 
cement. 

325. Methods of Treating Feed Waters, (a) A large quan- 
tity of the material carried in solution in boiler feed waters can 
often be precipitated by simply raising the temperature. This 
should be done in open type heaters using exhaust, or live steam, 
whichever is necessary to attain the necessary temperature. 
The impurities which are precipitated either remain fastened 
to the pans and other parts of the heater or are separated by 
filtering through a bed of coke, or other material, contained 
within the heater itself. 

(b) Where the use of live steam is not desirable or where the 
water contains salts that are not readily precipitated by simply 
raising the temperature, certain chemicals can be added to the 
water. These chemicals should be so chosen as to react with 
the majority, or with the most harmful, of the impurities to form 
insoluble precipitates, or to form less harmful, soluble com- 
pounds. By far the most common chemical in use for this 
purpose is soda ash (impure sodium carbonate) although various 
other inorganic and organic compounds are also utilized. Soda 
ash has the advantages of very low cost, small weight required, 



688 HEAT-POWER ENGINEERING 

applicability to most waters and formation of compounds which 
are easily disposed of in the heaters and in the boilers. 

(c) In many cases, particularly where steam is not available, 
or where special conditions are to be met, cold methods are 
used. In such cases a solution of the proper chemical, or chemi- 
cals, is fed in measured quantities to the raw water, and any 
precipitates formed are settled or filtered out, after which the 
treated water passes to some sort of storage to await use. 

Apparatus of this type is generally made wholly or partly 
automatic. It is always of large size and therefore costly, and 
because of the low temperature many reactions which may be 
easily carried out in heaters are either entirely absent or are 
very incomplete. 

(d) Many " boiler compounds,'^ some of secret composition, 
are in use. They are mixed with the feed water on its way to 
the boiler and are supposed to prevent or mitigate the formation 
of scale. It should be remembered that no solid material which 
enters the boiler can leave with the steam and hence it must all 
remain within the vessel unless removed by other means, such 
as blowing down, skimming, etc. 

This being the case, all that can be expected of a boiler com- 
pound is that it will react with the most troublesome impurities 
so as to change them to less troublesome ones which can be 
removed as sludge through the blow-off valve, rather than as a 
hard scale adhering to the metallic surfaces. In any event the 
amount of solid to be removed from the boiler will be greater 
when a compound is used than when the untreated water is 
vaporized, and it is merely a question of whether the greater 
amount of soft material permits of more economical and safer 
operation than does the smaller quantity of harder scale. It 
is therefore obvious that the impurities should, when possible, 
be removed from the water before it is introduced into the 
boiler. 

(e) There are some so-called " boiler compounds " on the 
market which are not supposed to react with the solids in the 
water but are intended to coat the water side of all heating sur- 
faces in such a way as to prevent the adherence of scale and 
scale-forming material. Besides the commercial compounds, 
kerosene and similar hydrocarbon oils have been more or less 
successfully used for this purpose. Oil so used should contain 



WATER PURIFICATION 689 

no organic admixture as this may cause trouble by saponifying 
in the boiler and it should contain no heavy hydrocarbons 
which will form tar or pitch as these might cause overheating of 
plates to which they become attached. 

It has also been claimed that graphite acts in a way similar to 
kerosene in preventing the adherence of scale-forming material. 



CHAPTER XXXIX. 



POWER PLANTS. 



326. General, (a) Only a very general discussion of the sub- 
ject of power plants as a whole can be attempted in this book 
and that must be given in the briefest manner possible. Plants 
having internal combustion engines and those having steam- 
operated prime movers will be the only types considered. 

(b) The choice between plants of these two types depends on 
many considerations, some of which are: (i) kind of fuel avail- 
able, (2) fuel economy, (3) first cost and other financial con- 
siderations, (4) reliability, (5) weight, (6) space occupied, (7) 
cost of water, (8) ability to secure properly trained attendants, 
(9) location, and (10) character of load. In general, where 
coal is very expensive, the producer plant will give better finan- 
cial returns than a steam plant unless the power requirements 
are such as to call for unusually large units (say, from looo to 
4000 or 5000 horse power for the plant) . 

327. Internal Combustion Engine Plants. If the fuel is oil, 
or gas, the plant merely consists of the engine with means of 

supplying the fuel and for 
transmitting the energy de- 
veloped, and with provision 
for jacket water. If solid 
fuel is used in a producer, 
the elements of the plant 
are those given in Fig. 443. 



328. Steam Power 
Plants, (a) The location 
of the plant is selected with 
respect to (i) railroad and 
dock facilities for receiv- 

(2) supply of water suitable 

(3) convenience for distribu- 





Fuel 






> ^ 1 

1 Proauee. | 






. ^ . 






1 En..ne 1 




/ 






Product 
(Electric Energy) 



Elements of a Producer Gas 
Power Plant. 



ing coal and disposing of ashes, 
for feed and condensing purposes, 

690 



POWER PLANTS 



691 



tion of its products (electrical energy, exhaust steam for heating, 
belt delivered power, etc.), (4) cost of real estate, (5) suitability 
of ground for foundations, (6) space for storage of fuel, (7) char- 
acter of the surrounding neighborhood, and (8) allowance for 
increase in size of plant. 

(b) The building is generally divided by a fireproof and dust- 



'Jr>^ Energy Supply 




Fig. 444. — Elements of a Steam Power Plant. 



proof wall into the boiler room and the engine (or turbine) room, 
and is provided with proper lighting and ventilating facilities 
and with doorways of sufficient size to admit the largest pieces 
of the equipment. In large plants the railroad track usually 
enters the building, the doors being large enough to admit box 
cars. The architecture of the building should be in harmony 



692 



HEAT-POWER ENGINEERING 



with its surroundings and the design should, in general, permit of 

enlargement of plant to meet increases in the demand for power. 

The scheme of the steam power plant equipment is illustrated 

in Fig. 444. This diagram is very general and includes pieces 

of equipment which are 
used only in special cases; 
it also shows apparatus 
which would not, in gen- 
eral, be used at the same 
time in ordinary cases. 
Several arrangements of 
steam power plants are 
shown in Figs. 445 to 449. 
(c) In the boiler room, 
besides the boilers, are lo- 
cated the feed pumps, fans, feed heaters (generally), economizers, 
etc. Car tracks are arranged to deliver the coal at such point as 
to reduce the manual labor to the minimum. Large plants usu- 




Fig. 445. — Small Engine Plant. 




Fig. 446. — Small Turbine Plant. 



ally have overhead bunkers, to which the coal is brought by cars 
or by mechanical conveyors of the bucket, belt, or other type, and 
from which chutes lead to the hoppers of the stokers, or, in case 
of hand firing, to the floor in front of the boiler ; and ash hoppers 



POWER PLANTS 



693 



are generally placed under the grates with dumps discharging 
to conveyors or cars below. In some instances boilers are 
located on two or more floors (as in "double deck" plants) as in 




Fig. 447. — Large Turbine Plant. 



Fig. 448, or are fired from both ends (Figs. 367 and 449), to re- 
duce the ground area occupied. These special arrangements are 
more often adopted in turbine plants than in those having engines, 



694 



HEAT-POWER ENGINEERING 



because the turbine room is generally much smaller than the boiler 
room, whereas an engine room is ordinarily of about the same size. 
(d) The larger engine rooms are usually provided with over- 
head traveling cranes of capacity at least sufficient to lift the 
heaviest piece of machinery. Surface and jet condensers and 
their pumps are usually located below the engine, in the base- 




Fig. 448. — Power Plant with Double Deck Boiler Room. 



ment; and barometric and siphon condensers are often placed 
outside the building. 

(e) In electric plants as much of the steam piping as is feasible 
is located in the boiler room to prevent liability of damage to 
the electrical apparatus by the steam in case of pipe failure. 
Where plant shutdowns are of serious consequence, the ideal 
arrangement of piping would permit (i) of running any prime 
mover from any boiler, (2) of any boiler, or engine unit, being 
isolated without affecting the rest, and (3) of making repairs 
to any portion of the piping without affecting any unit (or not 
more than one). This ideal case is approximated most closely 



POWER PLANTS 



695 



by the "loop or ring'' system of piping, a in Fig. 450, and 
by the "double-header" system, as b in Fig. 450. These systems 
call for an amount of piping and a number of joints and valves 
that is prohibitive in most cases. Ordinarily the connections 
from the boilers are merely led to a "single header" from which 
other pipes lead to the prime movers, as c in Fig. 450. In large 
plants it is common practice to arrange each prime mover and 




Fig. 449. — Power Plant with Boilers Fired from Both Ends, and with Com- 
pound Steam Engines Exhausting to Low Pressure Turbines. 

the boilers which serve it, as an independent unit; but fre- 
quently cross-connections are provided between units for use in 
emergencies. There is almost an unlimited number of arrange- 
ments of piping possible, but they are generally modifications 
or combinations of those just given. 

The piping for the auxiliary apparatus is independent of the 
main system to permit that apparatus to be operated even 
though the other is not in use. 



696 



HEAT-POWER ENGINEERING 



The steam pipes from the boiler have hand-operated shut-off 
valves, and in some cases also include emergency valves which 
will close if abnormal outflow of steam occurs, as when a steam 
pipe is ruptured, and act as check valves preventing the inrush 



^M 



(a) 




X3 



s 



t^ 



(«) 



Fig. 450. — Steam Piping Arrangements. 



of steam from other boilers if a tube fails. The engine feeders 
also have shut-off valves near the cylinders and sometimes there 
are also valves which will automatically close if the engine starts 
to run away. All steam piping should be lagged with non- 

T By-pass 



Economizer 




Hot Well Water 
or Raw Feed 



conducting covering; it must be properly supported; provision 
for expansion must be made by the introduction of slip or swivel 
joints, corrugated sections or flexible curved portions; and it 
must be so arranged as to be without undrained portions from 
which the collected water can be carried over in large quan- 
tities to the prime mover with disastrous results. The piping 



POWER PLANTS 697 

should be properly drained by suitably arranged collecting 
pockets connected with "traps" or equivalent devices and at 
the engines there should be "steam separators." The traps (by 
float or other device) automatically discharge the accumulation 
of water from time to time. 

(f) The boiler feed-water piping is preferably so arranged that 
any of several pumps (or injectors) can be used for supplying 
the feed water, and also so that there are several sources from 
which this water can be obtained. One of the numerous possible 
arrangements of piping is diagrammed in Fig. 451. 

(g) Each piece of auxiliary apparatus is preferably so arranged 
that it can serve any one of the sets of main units, and so that 
it can be isolated if out of commission and the materials which 
it ordinarily handles may be by-passed around and led direct to 
their final destinations. 



CHAPTER XL. 

CONTINUOUS FLOW OF GASES AND VAPORS THROUGH ORIFICES 
AND NOZZLES. 

329. Introductory, (a) The thermodynamic transformations 
previously discussed in this book were assumed to occur in such 
manner that the change of kinetic energy (velocity energy) 
associated with the flow of the working substance from one part 
of the system to another was zero. In the usual cases of flow 
of gases or vapors through pipes and in cylinders this same 
assumption may be made without introducing serious error, 
because of the relatively low velocities prevailing. 

When, however, gases or vapors flow through nozzles or ori- 
fices both the changes in velocity and the corresponding changes 
in the kinetic energy of the working substance may be very large. 
In such instances much of the potential energy associated with the 
substance may be converted into the kinetic energy associated 
with the change of motion, or the reverse process may occur. 

(b) Let Fig. 452 represent a conduit through which the ma- 
terial flows in the direction of the arrow; and let Po and K 
■^ , be respectively the simultaneous poten- 

v-^iPs ^-g^j ^^^ kinetic energies associated with 




a pound of the working substance at any 

^. instant. Then Poi -f Ki is the total 

Fig. 452. 

associated energy per pound when the 

stream passes section i in Fig. 452 and Po% + K2 is its value 

when passing section 2. If the conduit is of such character that 

energy neither passes through, nor is stored by, its walls, it 

follows from the Law of Conservation of Energy, and from the 

First Law of Thermodynamics, that 

Poi + Ki = Po, -\- K2, (494) 

from which AK = K, — Ki = Poi — Po, .... (495) 

where AX is the Change in Kinetic Energy per pound of mate- 
rial. This equation shows that the changes in kinetic and 

698 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 699 

potential energies between sections i and 2 are equal in amounts 
but opposite in direction. 

(c) For the purposes of analytical development it is desirable 
to examine more in detail the character of the potential energy 
which must be considered in connection with the flow of gases 
and vapors. One form of potential energy is that due to posi- 
tion, as exemplified by the familiar "head" in hydraulics. In 
most engineering problems dealing with the thermodynamics of 
flow of the materials under consideration the magnitude of this 
form is so small that it may be neglected without serious error. 
A second form is that due to a substance's stored heat energy which 
was expended in raising the sensible heat of the material, or in 
doing internal work, or in both; and it is obviously composed 
of the AS and A/ which have been used before. The only other 
form of potential energy is that stored in the enveloping media 
due to external work done upon them by the substance sur- 
rounded. Although stored in the surrounding media, it is con- 
venient to consider this potential energy as associated with the 
substance that did the work, because in all cases this energy 
would be returned if that substance were brought back to the 
original conditions. Evidently this stored external work cor- 
responds to the AE used in previous discussions, but for subse- 
quent purposes it will be convenient to obtain a slightly different 
viewpoint regarding it. 

(d) For this purpose suppose the plug a (in Fig. 453), weighing 
one pound, and having a (specific) volume V, is injected its full 
length into a closed vessel b which is so large 
that the medium it contains may be assumed 
to remain at constant pressure P pounds per 
square foot during the process. Then, the 
external work done by the plug upon the 
medium is PV foot-pounds, or PV/778 B.t.u. 
This energy is stored in the surrounding 
medium, but as it will be returned when the 
plug is withdrawn, it may be considered to 
be associated with the plug. Obviously all ^^' ^^^' 
material, which is surrounded by media upon which it has 
done work which is stored as potential energy of this form, 
may be considered as having associated with it this returnable 
energy, 




700 HEAT-POWER ENGINEERING 

(e) Now, summing up, the total potential energy which may 
be considered as associated with a pound of the material is 

Po = ^S + M + PW/77S .... (496) 
measured above certain datum conditions which will be consid- 
ered later. 

This value of the potential energy may now be substituted in 
Eq. (494) giving, for the conditions of flow shown in Fig, 452,, 

(A5i+A/i+PiVi/778)+i^i = (A52+A/2+P2V2/778)+i^2, (497> 
and Eq. (495) then becomes 
AK = (K2 - Ki) 

= (A5i + A/i + PiVi/778) - (AS2 + A72 + P2V2/778). (498)' 

The change in kinetic energy AK, and hence the change in 

velocity, between sections i and 2 can thus be computed when 

the intrinsic energies (AS + A 7) and the PV conditions of the 

material as it passes these sections are known. 

(f) U w pounds of substance are flowing per second with a 
velocity of v feet per second, the kinetic energy of the flowing 
material is wK = wv"^ -7- (2 g X 778), or the kinetic energy per 
pound is 2 

^ = 17x778 •'■'•" («9) 

If the velocity is increased from Vi to V2, the change in kinetic 
energy is, per pound of substance, 

Air=(i^2-i^i)=(^-|^)/778B.t.u. . (500) 

But since (K2 — Ki) = (Poi — P02) this "equation may be re- 
written / 2 7.2\ 

AK = Po,- Po2={^^^- ^y 778 B.t.u., . (501) 

which may be used for determining the velocity changes when 
the changes in potential energy are known. 

330. Flow of Saturated Steam in the Ideal Case, (a) Fol- 
lowing the general equation (498), the kinetic energy change 
during flow, in terms of the change in potential energy, is 

AK = (a5. + A/, + f|')-(A& + A/. + ^). 

and as the right hand side of this equation represents differences 
between the various heat quantities, it is immaterial what is 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 701 

taken as a datum. It is therefore convenient in the case of steam 
to use 32 degrees F. as such. With this assumption it is obvious 
that for saturated steam which is initially dry A5i and A^2 
must equal qi and ^2; A/i and A/2 must equal pi and X2P2; and 
-PiVi/778 and P2V2/778 correspond to {APn)i and {xAPu)2 if 
the volume of water be neglected, which is permissible since it 
is relatively insignificantly small. The general equation for 
saturated steam may therefore be written in the form 

AK = (q-\- p-h APu)i - (g + xp + xAPu)2 
= (5+O1- {i + xr)2 
= A(2i-A(22, (502) 

in which AQi and AQ2 are the total heats above 32 degrees per 
pound of steam at points i and 2 respectively. 

While the foregoing discussion considered only the case of 
dry saturated steam, it applies equally as well to any initial 
condition. Thus in the ideal case AQi is the total stock of heat 
per pound of steam entering the nozzle and AQ2 is that remain- 
ing when the lower pressure is reached by the process of ex- 
pansion. 

It is obvious that even though the initial and final pressures 
are known, Eq. (502) cannot be used for the solution of numerical 
problems until some means is found for determining the value 
of X2, or AQ2. But after they have been found AK can be deter- 
mined; then from Eq. (501) the change in velocity of flow can 
be computed. Methods of determining the values of X2 and AQ2 
will now be considered. 

(b) Since the velocity of steam flowing through a nozzle or 
similar conduit is very high there is very short time of contact 
between steam and walls. And further, since the temperature 
of the steam in contact with any particular ring in the wall of 
the conduit is always the same so long as steady conditions 
are maintained, it follows that each part of the wall will acquire 
practically the same temperature as the steam in contact with 
it. As a result of these two facts there is in a real case very 
little transfer of heat between the walls and the steam and 
it is reasonable to assume no transfer in an ideal case, hence 
the flow may be considered an adiabatic process, or, since the 
pressure decreases as flow progresses, as an adiabatic expan- 
sion. 



702 



HEAT-POWER ENGINEERING 



It can also be shown that for ideal conditions this adiabatic 
expansion may also be treated without serious error as isen- 
tropic, consequently all the mechanism previously developed for 
such conditions can be used in this case. 

(c) Then, on the T<^-diagram in Fig. 454, if the initial state 
point is I (the condition being Ti, Xi, A<3i), the ideal expansion 

in the nozzle would be along the isen- 
tropic line to point 2 where the condi- 
tion is T2, X2, A (22- The heat AQi per 
pound of steam at the beginning of 
expansion is shown by the area sur- 
rounded by the heavy line; and the 
heat AQ2 at the end of the process, by 
the sectioned area ; hence the net work 
AK done is AQ1 — AQ2 and is shown by 
area abi2. This area is seen to equal 
that surrounded by the lines of the 
Clausius cycle. Hence, in the ideal 
case the change of kinetic energy AK 
occurring in a steam nozzle is equivalent to the external work, 
AE = {AQi — AQ<^, done with a Clausius cycle having the same 
expansion line and using the same weight of material. 

Thus AK (= A£ = AQx - AQ2) can be computed by the 
methods given in Sect. 94 for determining the work of the Clausius 
cycle, or it can be obtained from the 
T(^-diagram or from the Mollier Chart. 

(d) On the Mollier Chart, Fig. 455, 
the ideal (isentropic) process for one 
pound of steam is represented by the 
line 1-2. At the initial point the con- 
dition of the steam is Xi, pi, AQi; and at point 2 it is X2, p-i, 
AQ2. During the process heat equal to AK = {AQx — AQ2), as 
shown by the length 1-2, is surrendered for producing the flow. 

(e) Having found AK = {AQi — AQ2), .the velocity of the 
stream passing point 2 is, from Eq. 501, 

• (503) 






AQi 



A.Q2 



Fig. 455- 



V2 



\/vi^ -h 50,103 X Ef (A(2i - AQ2) ft. sec. 



in which Ef is the efficiency of heat conversion as compared 
with the ideal case. Its value is of course unity when no losses 
occur. 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 703 

If the acceleration is from rest, or from a negligible initial 
velocity, which is ordinarily the case, then Eq. (503) becomes 

V = 223.8 V£/(A(2i - A(22) ft. sec, . . . (504) 
or V = 223.8 VEf X ^K ft. sec (505) 

(f) If the velocity of the stream is v feet per second at any 
section which has an area of a square inches, then the volume 
flowing per second through that section is (va/i/^^.) cubic feet; 
also if w pounds of material are passing the section per second, 
and if the specific volume is V * and the quality x, then the 
volume passing per second is wxV. Hence, at the given section 

wxV = i'a/144 (506) 

Thus, if a given weight of vapor, of known specific volume and 
quality, is to be passed with a given velocity, the area of the 
passage must be ^^y 

^ = -^ X 144 (507) 

Or the weight of the material passed by a given area may be 
computed from ^^ 

w = — (508) 

144 xY ^ ' 

While the foregoing discussion was confined to steam, it, of 
course, applies equally well to any other vapor. But these 
equations cannot be applied indiscriminately as will be shown in 
the next section. 

331. The Ideal Steam Nozzle, (a) Starting with any initial 
state {p\X\LQx) and expanding in a steam nozzle in the manner 
described, it will be found that as the terminal pressure is 
lowered certain peculiar phenomena occur which are difficult 
to understand without the aid of curves. These curves will 
now be constructed: 

For a series of such expansions, all for one pound of steam 
and from a fixed initial absolute pressure p\ and quality X\, to 

* The weight of the steam per pound of material is equal to the quality x and 
that of the moisture is (i — x); the volume of the steam is xV and that of the 
water is (i — a;) X volume of i pound of water. As the volume of one pound of 
water is about xeVo that of the steam at atmospheric pressure and of like order at 
other pressures the volimie occupied by the moisture in the steam is negligible and 
hence is not included in the discussion given above. 



704 



HEAT-POWER ENGINEERING 



progressively decreasing absolute pressures p, let there be de- 
rived the successive values of: 

(i) The quantities x at pressures p; 

(2) The heat ^K = AQi - AQ theoretically made avail- 

able for producing flow; and 

(3) The specific volumes V at pressure p. 

Items (i) and (2) may be readily obtained from the Mollier Chart 
or they may be computed by the methods given in Sect. 94; and 
(3) may be obtained from the steam tables. Then with the values 
of AK as abscissas plot curves, as in 
Fig, 456 (a) , to show by ordinates how p, 
X and V change with the surrender of 
heat as the expansion progresses. 

Next compute the progressive values 
of 

(4) The actual volumes (xV) of one 
pound of material ; 

(5) The jet velocities v (by substi- 
tuting the different values of 
(A(2i - A(2), in Eq. (504)) ; and 

(6) The areas a of sections required 
at different points along the 
nozzle to obtain these veloci- 
ties. These areas may be ob- 
tained from Eq. (507). 

Then with the same abscissas as before 
plot curves, as in Fig. 456 (b) to show 
by ordinates the variation of xV, v and 
a with AK. 

(b) Now referring to the figure it will be seen from the a-curve 
that, as expansion progresses, the cross-sectional area of the 
passage must at first contract and then diverge, if expansion 
is carried far enough, — thus the nozzle must have a neck. Pro- 
jecting upward from this neck to the p-curve, it will be found 
that the neck pressure is about 58 per cent of the initial pressure 
and that the corresponding point Vn on the z;-curve will scale at 
a little over 1400 feet per second. And it is important to note 
that about these same values will always obtain regardless of 




Fig. 456. 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 705 

the initial condition of the steam,* hence they are called the 
critical pressure and critical velocity. 

(c) Fig. 456 (c) shows the longitudinal section of a nozzle in 
which the amount of heat surrendered per inch of length is 
constant from one end to the other and is equal to the abscissa 
scale used for the curves above. This nozzle is for one pound 
of steam flowing per second, with terminal pressure p2 pounds 
absolute and final velocity V2, as shown on the respective curves. 
Corresponding to any other pressure of exit from the nozzle, 
the end diameter may be found by projecting downward from 
the proper point on the ^-curve to the longitudinal section of 
the nozzle; — thus for discharge to atmospheric pressure (14.7 
lbs.) the end diameter is seen to be d^, the length of nozzle is 
l^, and the terminal velocity is Vj^; for discharge to a pressure 
pn = .58^1 the corresponding values would be dn, In and Vn] 
and for terminal pressure equal to pB they would be dn, Ib and 
vb- Evidently a nozzle originally used with discharge pressure 
p2 will be theoretically correct for a case where the pressure is 
atmospheric, if its end is cut off sufficiently to have the final 
diameter beyond the neck equal to d^, and similarly for the 
other terminal pressures. Thus regardless of the exit pressures, 
Fig. 456 (c) is the horizontal section of all nozzles discharging the 
same weight of steam per second with same initial conditions, 
the only difference between the various nozzles being in. the 
lengths and end diameters, which are made to correspond to 
the terminal pressures. 

(d) The reason the neck is present in all cases where the ex- 
pansion is to a pressure below .58 pi can now be easily explained : 
From Eq. (507) the area of the nozzle at any section, per pound 
of material flowing per second, is 

xV 
a = — X 144. 

V 

Now referring to the curves for xV and v in Fig. 456 (c) it will 
be seen that as the expansion progresses the numerator xV at 
first increases much slower than does the denominator v, and 
hence the nozzle areas {a) must first diminish; but that later 
the conditions are reversed, consequently the areas must then 

* There will be slight variations with the initial conditions, but these are not 
great and will not be discussed in this elementary treatment. 



706 HEAT-POWER ENGINEERING 

increase. Obviously there must be a neck where the converging 
and diverging portions of the nozzle join. 

(e) It has been seen that, corresponding to each cross section 
of the nozzle, the steam has a definite condition and velocity, as 
shown by the ordinates in Fig. 456 immediately above the sec- 
tion under consideration. If the cross sections of the nozzle 
were shifted or spaced differently, so as to alter the longitudinal 
section of the nozzle from that shown, the ordinates of the 
curves would be similarly shifted and the character of the 
curves would change. This shifting may be so done as to cause 
any one of the curves to become a straight line ; thus the nozzle 
may be such as to cause a uniform drop in pressure throughout 
its length, or a uniform increase in velocity, or a uniform in- 
crease in volume, whichever is most suitable for the purpose in 
hand, or any line can be made to have any desired curvature. 

Usually nozzles are made with rounded entrance like that 
shown, but with straight conical divergence, as in Fig. 457, as 
this form is easiest to make and appears to be 
about as efficient as any. The stream lines of 
the jet issuing from such a nozzle are practically 
parallel, which is important if the jet is to act 
Fig. 457. on turbine blades. For such a nozzle it is only 

necessary to compute the areas of the neck and 
discharge end; the entrance is then made rounded and the 
diverging portion is conical, the length depending on the angle 
of divergence, which should not be too great. 

(f) With a given nozzle (ideal or approximately such) it is 
found that, accompanying a lowering of the pressure against 
which it discharges, the velocity of flow increases until that 
through the smallest section (or neck) reaches the critical value 
(the pressure then being the critical one) and that any further 
diminution of the pressure does not change the velocity and 
pressure at that section, nor does it increase the weight of mate- 
rial flowing per second through the nozzle. Hence, if the ter- 
minal pressure is below .58 pi, the area of the neck and the 
critical velocity will fix the amount of material flowing per 
second. If merely an orifice with rounded entrance is used the 
discharge velocity will be the critical regardless of the pressure 
against which the jet issues, provided it is below the critical. 
After the steam has once passed the neck it can further expand 




CONTINUOUS FLOW OF GASES THROUGH ORIFICES 707 

in a properly proportioned nozzle and can acquire in the diverg- 
ing portion of the nozzle an increased velocity of any desired 
amount (theoretically), its value merely being dependent on 
the terminal pressure. 

332. Actual Steam Nozzles, (a) It will be remembered that 
adiabatic conditions are those undef which the working sub- 
stance, while undergoing a thermodynamic change, neither re- 
ceives nor surrenders heat as such. 

It has already been shown that in the actual case of flow 
through nozzles the conditions are practically adiabatic, for the 
time of contact of each particle with the wall is infinitesimal 
and, with continuous flow in one direction, each portion of the 
nozzle wall becomes heated to the temperature of the contiguous, 
fluid and remains at that temperature; hence, neglecting radia- 
tion and conduction, there is no temperature head to produce 
heat transfer. 

(b) But although the conditions are adiabatic the expansion: 
process is not necessarily the equivalent of an isentropic one. 
In fact, it is possible to obtain adiabatic conditions of expansion, 
from the higher pressure to the lower one, under which none 
of the potential energy may be converted into kinetic energy of 
a flowing stream. For example, if the expansion is through a 
porous plug with pressure drop, the velocity of flow is negli- 
gible and, as has already been seen, the total heat A.Q2 per pound 
of working substance at the end of the process is equal to the 
amount AQi it had at the beginning, hence AQi — AQ2 = o 
and AX = o. This expansion from the higher to lower pressure 
is along the constant heat lines on the T(/)-diagram and on 
the Mollier Chart and is accompanied by increase in entropy. 
This is a case of resisted flow, and it can be considered that, for 
each slight pressure drop, some of the intrinsic energy (8S + 81) 
of the material is expended in producing velocity (8v) of flow 
through a short length of plug, but that the friction and eddy 
currents reconvert this energy (8K) of flow back into heat (8Q) 
which is returned to the fluid and brings its stock back to the 
original value. Throttling of steam is a similar process. 

(c) Between the constant heat expansion (with AK = o) 
and the isentropic one (with AK = AE) there may be an un- 
limited number of processes even though under adiabatic con- 



7o8 



HEAT-POWER ENGINEERING 



ditions. It is, of course, desirable to so proportion the nozzle 
that it will offer no resistance to expansion, and cause no eddying, 
also that it will deliver the material in parallel stream lines. If 
this is effected the ideal conditions exist and the expansion is 
equivalent to isentropic. 

(d) With resisted flow the velocity of the steam can be com- 
puted by using Eq. (505) „and Introducing the efficiency coeffi- 
cient Ef, the proper values of which depend on the character, 
extent and shape of the guiding walls, and on the velocity, 
density and quality, or superheat, of the steam. The values of 
Ef range from .85 to .97 in nozzles used in turbines, 

(e) The case of resisted flow is shown on the T(i>-diagram in 
Fig. 458, the heat LQ\ initially associated with each pound of 

working substance being shown by the 
area surrounded by the heavy line. If 
the expansion were ideal, from i to 2, the 
heat LQ2, at temperature Ti, remaining 
in the material after the process would be 
shown by the area below ab2. However, 
with resisted flow to the same lower tem- 
perature, T2, less heat than the ideal 
amount is abstracted ; hence more heat (of 
total amount A (22') remains associated 
with the material, its amount being shown 
by the sectioned area. The final state point is then at 2'; the 
quality is x-z , which is higher than X'l as would be expected, and 
02 is the entropy, which is greater than 0i. 

Evidently the heat available for accelerating the jet is AX' 
= (AQi — A(22') which may be used under the radicals in Eqs. 
(504) and (505) to obtain the velocity of flow for this case ; after 
which Eqs. (507) and (508) may be used in the same manner as 
before. If £/ is the efficiency of conversion then Ai^' = Aii^ X 
Ef, where Ai^ is the energy theoretically available in the ideal 
case. In the T0-diagram there is no one area representing this 
available energy Ai^' ; it is merely shown by the difference be- 
tween the area surrounded by the heavy line and that which is 
hatched. 

(f) The Mollier diagram for resisted flow Is shown In Fig. 
459. With ideal expansion from state point i to 2, the heat 
per pound of steam would change from AQi to A(22, the heat 




Fig. 458. 




CONTINUOUS FLOW OF GASES THROUGH ORIFICES 709 

surrendered would be AK = A(2i — AQ2, and the final quality 
would be X2. With resisted expansion to the same terminal 
pressure, p2, more heat, ^.Q^' (> A(22), remains in the steam than 
in the ideal case (as less is abstracted) and the final state point 
is found at the intersection 2' of 
the constant heat line of AQ2' 
with the pressure line p2. The 
final quality X2' ( > X2) and en- 
tropy 02 ( > </>i) are determined 
by \ the quality and entropy 
lines passing through point 2'. 
The heat converted into kinetic energy is AK' = AQi — AQ2 
(< AK), and as before AK' = AKX Ef. This value of AK' 
is then used in the manner described at the end of the preceding 
paragraph. 

(g) The values of AK' and X2 may also be found by compu- 
tation. First AK for the ideal case is determined by the methods . 
given in Sect. 94 for the Clausius cycle. Then with Ef assumed, 
AK' is AK X Ef, and the heat remaining per pound of steam at 
the end of the process is 

A(22' = A(2i - (Ai^ X £/) (509) 

Since AQ2' = X2H + 52, it follows that 

X2' = (A(22' - 22) 4- r2, (510) 

where 52 and ^2 correspond to the known terminal pressure. 
The final entropy is then 

<^2 = <A..+'|^, (511) 

J 2 

in which all quantities on the right-hand side of the equation 
are either known or can be obtained from the steam table. 

(h) The purpose of the foregoing discussion is merely to pre- 
sent the fundamental thermodynamic theory underlying the 
flow of steam at high velocities through nozzles and orifices. 
A detailed discussion of the subject cannot be attempted in 
this book and for further study the student is referred to any of 
the numerous textbooks on Steam Turbines. 

333. Empirical Formulas for the Flow of Steam through Ori- 
fices, (a) It is sometimes "convenient to have simple empirical 
formulas for quickly determining the approximate velocity of 



7IO HEAT-POWER ENGINEERING 

discharge from a given orifice, or for obtaining the area of orifice 
required for discharging a given weight of steam per second, 
when the discharge pressure is below .58 pi. The following two 
formulas apply to such cases when the orifice has a properly 
rounded entrance, and they also apply to the neck of a diverging 
nozzle. 

(b) Napier's experimentally determined rule gives the pounds 
of steam, initially dry, flowing per second from an orifice to be 

w = {p X a) ^ 70, (512) 

or the area, in square inches, is 

a = 7ow-^p, (513) 

where p is the absolute pressure in pounds per square inch. 

(c) A slightly more accurate but less convenient formula is 
that due to Grashof. For steam initially dry it is 

p-^'^a , , 



,97 ' (515) 



from which 

60 w 

P 
the notation being the same as in (b). 

334. Flow of Steam through Pipes, (a) The law for the 
frictional resistance accompanying the flow of steam through 
pipes resembles closely that expressed in Eq. (409) which shows 
that the resistance is directly proportional to the length of pipe, 
perimeter of cross section, character of surface and square of 
the velocity, and inversely to the area of section. To overcome 
this resistance and the inertia of the fluid there must be a drop 
in pressure from the entrance to the pipe to the discharge end. 
As the resistance varies with the square of the velocity, the 
pressure drop increases very rapidly as the velocity is made 
greater. Hence in practice the velocities used in pipes are very 
low, as compared with those in nozzles where the short length 
makes the loss by resistance very small even though great 
velocities are used. 

(b) While the same treatment that is used for nozzles might 
be applied to pipes, the pressure drops and energy expended in 
producing the flow are so small that it is convenient to use 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 711 

another method which disregards altogether the quantity of 
energy expended and only considers the pressure drop that is 
involved. This method makes use of Eq. (410), which for round 
pipes becomes 

^^=i^/^^' (5.6) 

If W pounds of steam flow per minute, the volume flowing 
per second is the product of the weight per second (l^/6o) and 
the specific volume V, which is the reciprocal of the density 5. 
If the diameter of the pipe in inches is d, the velocity of flow 
is obviously v = (144 WW) -^ (60 7r^V4)- Substituting this in 
Eq. (516) and solving gives the pipe diameter in inches, 



-4 



W' ■■ ^^'^^ 



where 

W = pounds of steam flowing per minute, 
L = length of pipe in feet, 
V = specific volume of the steam, 
AP = pressure drop throughout the length of pipe, and 
c = a constant whose value is ordinarily .2, but this may be 
decreased slightly with very large pipes, as/ seems 
to diminish somewhat as the diameter is increased. 

The longer the pipe is made and the smaller the pressure drop 
allowed, the larger will be the diameter. But a larger diameter 
means increased first cost and greater heat loss by "radiation." 
Hence the diameter selected should be a compromise based on 
all these considerations. 

(c) If the allowable velocity (v^) of flow in feet per minute and 
the total volume (Vm) of steam to be transmitted in the same 
length of time are known, then the area of pipe in square inches 
immediately follows from 

a^'^^><^ (518) 

For steady flow in high-pressure steam mains Vm is generally 
about 6000 feet per minute for saturated steam, while with 
superheated steam, with the larger sizes of pipe, and with those 
of short length, somewhat higher values prevail. 

Exhaust pipes from turbines to condensers have velocities as 
great as 24,000 feet per minute and even higher in some cases. 



712 HEAT-POWER ENGINEERING 

(d) Steam engines receive and exhaust the steam intermit- 
tently and the area of pipes is commonly obtained by using Eq. 
(274) with V = 6000 to 7000 feet per minute for high-pressure 
live steam pipes and v = 3500 to 5000 for exhaust pipes. 

335. Application of Steam Nozzles. The largest field of 
application for steam nozzles is in steam turbines, which have 
already been considered. Another wide field is in Steam In- 
jectors, used for delivering feed water to boilers, and for similar 
purposes. This piece of apparatus, in its simplest form, is 
shown diagrammatically in Fig. 460. Briefly it operates as 




follows: Steam, admitted through valve V, acquires high veloc- 
ity in passing through the nozzle, is condensed by the water in 
the combining tube and drives the water through the delivery 
tube and check valve into the pipe leading to the boiler. Thus, 
the flow through the nozzle is similar to that in the ordinary 
case, and the kinetic energy of the jet is used for injecting the 
water into the boiler against the pressure existing there. 

Steam nozzles are also used for inducing draft in the stacks 
of locomotives and traction engines, the exhaust steam being 
used for the purpose, which results in a slight increase in the 
back pressure on the engine. 

336. Perfect Flow of Ideal Gas. (a) In order to apply the 
equations of Sect. 329 to the flow of gases, it is first necessary to 
determine the intrinsic energy, A^* (H- A7 = o), per pouncf of 
material. It was shown in Sect. 30 that during isentropic ex- 
pansion the work performed per pound of gas is, from Eq. (50a), 

p^Vi — P9V0 

778 AE = ^^^ ^-^ = 778 A^, 

" 7 — 1 

which is done at the expense of the intrinsic energy. If it is 
assumed that this same law prevails with expansion continued 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 713 

to P2 = o, then all the intrinsic energy is converted into external 
work. Thus, upon this assumption, the total intrinsic energy per 
pound of material is, in general, 

PV 

^^ = 778(T-.) (5.9) 

Then from Eq. (496) the potential energy per pound is (since 

A/ = O), f py V 

Po = (^ + PVJ-778 

= (7^ ^^^^-^778. . . . (520) 

This is measured above a datum of absolute zero of pressures 
and temperatures, but as all problems in flow involve only differ- 
ences in energies this fact need cause no inconvenience. 

(b) Substituting in Eq. (501), for points i and 2 in Fig. 452, 
the values of Poi and P02 in terms of Eq. (520), gives 



\2g 2g) 



7 
If vi = o, then the final velocity is 



(PiVi - P2V2). . . . (521) 



v^csj 



2g— ^(PiVi-P^V^), . . . (522) 



in which c is a discharge coefficient with value equal to unity in 
the ideal case. Substituting this value off in Eq. (508), with 
X = I, the weight discharged per second is 



All quantities on the right-hand side of this equation are gen- 
erally known at the outset except V2. This latter must be de- 
termined before a solution can be effected. With isentropic 
expansion its value is found from the relation P-Ni'^ — PNi' to 

beV. = V,0- 

(c) Substituting the value of V2 in Eqs. (522) and (523), and 
simplifying gives 



N/-7^-.l-(^f'} 



(524) 



714 HEAT-POWER ENGINEERING 

1 



-^-mms/^^^M'-(pyl- <-' 



From which the area needed to discharge a given weight is 

(526) 



As sections i and 2, in Fig. 452, may be located at any points 
along the conduit, or nozzle, it is possible to use these formulas 
to analyze the changes occuring between any two sections, or 
over the whole length of passage. 

(d) If a curve is plotted to show how v, in Eq. (524), varies as 
(P2/-P1) is decreased, it will be found that, as in the case of steam, 
the nozzle will have a neck if P2 is low enough, and that the 
velocity through this neck becomes a maximum when a certain 
value of P2/P1 is reached. By differentiating Eq. (524) and 
making dv/diP^/Pi) = 0, this maximum velocity is found to 
occur when _ji_ 

P'/P'-i::^^' (5^7) 

the value of which is .527 when 7 = 1.41. Thus in this case 
the maximum or Critical Velocity at the neck occurs when P2 
has been reduced to a critical pressure of .527 Pi. 

This phenomenon has been repeatedly verified experimentally. 
It is found, as with steam, (i) that at the neck the critical pres- 
sure is, in the ideal case, always about .527 Pi, provided the 
pressure beyond the neck is equal to or less than this amount; 
(2) that lowering the discharge pressure below the critical pres- 
sure changes neither the pressure nor the velocity at the neck; 
and (3) that the neck velocity and initial PV-condition deter- 
mine the maximum amount of working substance which can 
flow through a given orifice or nozzle. Equations (524) and 
(525) will therefore give the maximum ideal velocity and weight 
of discharge through a neck of given cross section if .527 is 
substituted for (P2/P1) ; and Eq. (526) can be used to compute 
the neck area required for discharging a given weight of gas, if 
similar substitution is made. 

(e) In Sect. 87 (f) it was shown that when steam expands isen- 
tropically, for an initial quality greater than 70 per cent, the 



CONTINUOUS FLOW OF GASES THROUGH ORIFICES 715 

process is represented quite accurately by the equation for the 
isentropic expansion of gas, with an exponent n equal to (1.035 + 
0.1 x), in which x is the quality fraction. Thus it follows that 
Eqs. (524) to (526) are applicable to the flow of steam through 
orifices if this value of n is substituted for 7. 

(f) When the quality is unity, n = 1.135, and if this value is 
introduced for 7 in Eq. (527) it is found that the maximum flow 
of dry saturated steam through an orifice occurs when P2/-P1 = .58 
(about) . This is the value found by the method given in Sect. 
331 and its correctness has been verified experimentally. 



337. Imperfect Flow of Gases, (a) The actual velocity and 
weight of discharge from an orifice, or nozzle, are of course less 
than the theoretical. There are a number of 
reasons for this : — The real gases differ some- 
what from the ideal ; friction prevents some of 
the available heat energy from becoming con- 
verted into kinetic energy of flow; some of the 
kinetic energy is wasted in producing eddy 
currents ; heat energy is lost by radiation and 
conduction; and, if an orifice has improperly 
shaped walls, the cross section of the jet at its 
neck may be less than that of the orifice, as 
indicated in Fig. 461. To make allowance for 
the contraction of area, and for the various 
losses, the discharge coefficient c is Introduced in Eqs. (524) to 
(526). The value of this coefficient varies from .56 for certain 
sharp-edged circular orifices to nearly unity in the case of a 
mouth with properly rounded entrance. 




Fig. 461. 



CHAPTER XLI. 
COMPRESSED AIR. 

338. Definitions, (a) Air compressors in the broadest sense 
are all devices used for raising the pressure of air, but technically 
the term is generally applied only to apparatus which raises 
the pressure to a comparatively high value, say some value 
between 25 and several hundred pounds per square inch. In 
extreme cases the pressure is increased to several thousand 
pounds per square inch. 

(b) Other devices, such as fans and rotary blowers, are really 
compressors but are seldom spoken of as such, principally be- 
cause the pressures attained are so small that the principal func- 
tion may be considered to be the propelling of air rather than 
its compression. 

(c) The term' Blowing Engines, or Blowers, is used to desig- 
nate certain apparatus used for compressing air to pressures 
between about 10 pounds and 30 pounds above atmospheric for 
use in blowing cupolas and blast furnaces. These are properly 
air compressors but because of the low pressures many of the 
difficulties attending compression to higher pressures are not 
met in their design. 

339. Elementary Air Compressor, (a) The essential parts of 
an ideal air compressor of the simplest kind are shown semi- 

compressea Air Discharge diagranimatically in Fig. 462, A being 

t ionecevve^^^^^^^^^^ ^l^g spring-closcd admlsslon or inlet 

^ J B valve, which opens inwardly, and B 

"\^ a Rod and-FiBton the spriug-closcd discharge valve, 

_^l sF Driven from Opening outwardly. In the simplest 

aUU^ U _ External Source ^ , -hi 1 1 

IfC\ ■ ^^®^ there will be no clearance, the 

.a I , piston just touching the cylinder head 

Fig 462 ^^ °^^ ^^^ °f ^^^ stroke. 

(b) Imagine the piston in contact 
with the cylinder head in the ideal case. By the application of 
an external force to the piston rod the piston can be drawn to the 

716 



COMPRESSED AIR 717 

right, and air will then enter the cylinder through valve A at 
atmospheric pressure Pi, according to the horizontal line ab, in 
Fig. 463. 

(c) When the cylinder has been thus filled with air, the piston 
may be driven back to the left. As soon as such motion starts 
the valve A will be closed by the light spring shown, and the 
air entrapped in the cylinder will then be ^j p^ 
compressed according to some law, as ^K 

shown by he, the final volume being dc. o | N^. 

There are two limiting conditions which — %2l j — Pi_j__^^/>_ 

may be imagined as existing during com- ^ vd^ ''^"^ 

pression : Fig. 463. 

(i) No heat may be removed from the 
air during the process, in which case the compression will be 
adiabatic (with rise in temperature) ; and 

(2) All the heat generated during compression may be re- 
moved, in which case the compression will be isothermal. 

All actual cases generally fall between these limits as will be 
seen later. 

(d) Imagine the discharge pipe to be connected to a closed 
vessel, "a receiver," in which is maintained a constant pressure, 
P2, equal toPc. Assume further that the action of this pressure 
upon the valve B, plus the action of the spring is such that a 
uniform pressure of Pc pounds per unit area of valve face will 
just balance it. 

Then when the piston has compressed the air to the pressure 
Pc the discharge valve will open (at c) and the continued motion 
of the piston will "discharge" the air at constant pressure, P2. 
as shown by the line cd. Thus, the piston will end its stroke in 
contact with the cylinder head, having discharged at pressure 
P2 all the air received at pressure Pi. 

340. Work Done in Compressor, (a) In Fig. 463, area abge 
shows the work done upon the piston during the outstroke by the 
entering air, ghcde represents that done by the piston on the air 
during the instroke, and the net work is shown by area abed. 

Thus the area of the "compressor diagram," or card, meas- 
ures the net work done by the piston upon the air, just as the 
area of an engine diagram measures that done upon the piston 
by the working substance. 



7l8 HEAT-POWER ENGINEERING 

The Compression Line. 

(b) In Fig. 464 are given two superposed diagrams, abed and 
abc'd, bothi from the same ideal compressor which is to compress 
to a pressure P2 = Pd the amount of air which originally oc- 
cupied the volume Vb cubic feet when at atmospheric pressure. 

._ip The compression line be is an isothermal and 

\ the line be' is an adiabatie. 

^■Jw It is evident from the figure that the dia- 

\V^ gram containing an adiabatie ' compression 

.__/l^^5i^— Pa line encloses more area than that having 
I j > ^ ~^ ^ isothermal compression, and hence more en- 
Pig 464. ^ srgy from some outside source will be re- 
quired per cycle. Obviously, the isothermal 
compression is the more desirable, other things being equal, the 
work saved over that with adiabatie compression being shown 
on the diagram by the area cbc'. The higher the compression 
pressure the greater is the ratio of the work done with adiabatie 
compression to that with isothermal. 

(c) With isothermal compression the temperature of the air 
at e and b is, of course, the same, but during adiabatie compres- 
sion the temperature rises according to Eq. (51), the final tem- 
perature being 

^'^ nr'-' .... (528) 



iW 



Vb 
in which r = ratio of compression = -^ • 

y c 

If the air with pressure P/ and volume V/ is cooled at con- 
stant pressure it will attain a volume Vc when the initial tem- 
perature Tb is reached. This is approximately what happens 
in most real cases, for after the cooling has occurred the air is 
in the same condition as though it had been compressed iso- 
thermally. It is therefore advisable to strive for isothermal 
compression if this can be attained, or approached, without 
entailing greater outlay than the cost of the work area ebe'. 

Formulas for Work. 

(d) From the diagrams of Fig. 463 and Fig. 464, the work 
done by the piston per cycle with isothermal eompression and no 
clearance is evidently 



COMPRESSED AIR 719 

Work = work on he + work on cd — work on ab, ft. -lbs. 

= PcVc \ogeY + PcVc - PbVb, foot-pounds. . .(529) 

With adiahatic compression the work is (Fig. 464) 
Work = work on be' -\- work on c'd — work on ab 

= P^'^'^' -^^^' + p/7/ _ p^Vb, foot-pounds. . (530) 
7—1 

With any compression curve expressible by the equation PF" 
■■ constant, the work per cycle is 

Work = work on be" + work on c"d — work on ab 

= ^^^^ ^-^' + Pc"V."-PbVb, foot-pounds. (531) 



341. The Effect of Clearance, (a) No real compressor can 
be operated with the zero clearance assumed for the preceding 
elementary consideration. There must always be a certain 
amount of mechanical clearance between cylinder head and 
piston to insure safe operation and there are always passages 
or ports of some sort between the valve faces and the inside of 
the cylinder. 

(b) In Fig. 465 is given an ideal compressor diagram for a 
machine with clearance volume Va = Vd- At the end of the 
discharge, that is, after the completion u;^^^^ 
of the constant-pressure process cd, the 
clearance contains Vd = Vd cubic feet 
of air at a pressure P2 = Pd- When 
the piston starts on the outstroke the 
inlet valve will be held closed by this 
pressure until the piston has moved volume 

out far enough to allow the clearance ^^' ^ ^' 

air to expand to atmospheric pressure according to some such 
process as da. When a is reached the inlet valve will open and 
during the remainder of the stroke external air will enter the cyl- 
inder, as in the previous case. Though the stroke of the piston 
is such as to make available the volume Vb — Va = Vs, the 
amount of air actually entering the cylinder will be Vb —Va = Vea 
and only a fraction of the stroke, equal to Ves/ Vs, has therefore 



720 HEAT-POWER ENGINEERING 

been usefully employed. Thus the volumetric efficiency of this 
ideal simple compressor must be 

VEf^^^ (532) 

Obviously the piston displacement of the compressor with 
clearance must be to that of the compressor without clearance 
in the proportion Ve/ Ves if both are to compress the same quan- 
tity of air per cycle, therefore the existence of clearance makes 
necessary a larger compressor to handle a given volume of air. 

Effect of Clearance upon Work. 

(c) In the ideal case it may be assumed that the expansion 
of the clearance air along da takes place according to the same 
law as the compression of the mixture of clearance air and 
cylinder charge along the curve be. Then, if the clearance air 
be imagined to be separated by a flexible diaphragm from the 
fresh charge, and to be used over and over again, it is evident 
that it will deliver just as much work when expanding from d 
to a as will subsequently be consumed in compressing it from 
a to d. Then the net work necessary per cycle will be only that 
required to compress the volume Ves of cylinder charge from 
pressure Pi to P2 and discharge it at P2. Therefore, in the ideal 
case the presence of clearance does not alter the net work which 
must be done per cycle. 

It should, however, be noted that since the compressor with 
clearance will be larger than that without, the friction losses 
and cost of the machine will be greater in the real case. 

342. Real Single Stage Compressor Diagram, (a) The real 
compressor differs from the ideal in many respects, chiefly be- 
cause the cylinder and piston cannot be made of heat-resisting 
materials, because the valves cannot be made to operate per- 
fectly, and because of the inertia of the air being handled. 

A diagram obtained from a real compressor is shown in Fig. 
466, superposed upon an ideal one for the same machine, the 
pressure of air being supposed to be raised from atmospheric 
(Pi) to a receiver pressure equal to P2. 

(b) The ideal card is drawn for isothermal compression of the 
clearance air and charge and with isothermal expansion of the 



COMPRESSED AIR 7 21 

clearance air. In the real case it is never possible to obtain 
isothermal compression with a reciprocating air compressor; 
instead, the compression line falls between the adiabatic and the 
isothermal and is expressible by the equation PV" = constant, 
with values of n varying from about 1.2 in extremely favorable 
cases to about 1.3 under rather unfavorable conditions. To 
obtain such a curve it is necessary to cool the air during com- 
pression, by the methods which will be 
considered later. For present purposes 
it is merely necessary to note that the 
air, and therefore the cylinder walls, 
will become heated during compression. 

(c) During expansion of the clearance 
air, this material will, in general, be in ' volume 
contact with walls which are at a higher '^' "^ 
temperature, hence it will receive heat during the process. 
Ordinarily the real expansion line for this air lies between 
an adiabatic and an isothermal, but in the average case it 
approaches more nearly to the latter. The real expansion line 
may then be assumed to have a shape and position similar to 
da' in the figure. 

(d) In the ideal case the admission valve would open as soon 
as the clearance pressure has decreased to atmospheric, but 
actually the pressure must drop somewhat lower to give an 
unbalanced pressure great enough to open the valve against its 
spring, its friction and inertia, and also to overcome the inertia 
of the air and the resistance to flow through the more or less 
restricted areas available. 

After the valve is open and the air is in motion there are gen- 
erally several oscillations of the valve and the air column, as 
indicated by the wavy suction line, after which the pressure set- 
tles down to an average value sufficiently below the atmos- 
pheric pressure to cause the inflow. The oscillation of the valve 
is known as "fluttering." 

(e) From the fact that the same machine has been assumed 
in both cases it is evident that the actual volume of air in the 
cylinder at the end of the suction stroke must be the same in 
each case. In the real case, however, the air has a lower pres- 
sure than it has in the ideal, and, in general, its temperature will 
also have been raised by the heated walls which are uncovered 



722 HEAT- POWER ENGINEERING 

by the piston, thus the actual weight present will be less than 
the ideal. This effect will be considered more in detail in a 
later section. 

(f) Starting at the point b', instead of b, the air in the real 
case will be compressed according to some law intermediate be- 
tween the adiabatic and isothermal and therefore steeper than 
the ideal, as shown by b'c' in the figure. 

(g) The discharge valve does not open until the pressure 
attained is slightly above that in the receiver and it behaves 
much like the suction valve and for similar reasons. The dis- 
charge line actually obtained will then generally look something 
like c'd' instead of cd. 

(h) The discharge valve will obviously not close suddenly at 
the end of the stroke, consequently the corner at d' may be more 
or less rounded, the exact point at which expansion of the clear- 
ance air starts being rather difficult to determine. 

(i) The net result of the operation of the real compressor has 
been to compress a smaller weight of air than that handled by the 
ideal machine and to require the expenditure of work in excess 
of the ideal, as shown by the greater area enclosed. 

343. Volumetric Efficiency, (a) The volumetric efficiency of 
the ideal compressor was shown to be Ves/Vs, the symbols refer- 
ring to Fig. 465. In a real case the determination of the volu- 
metric efficiency is not as simple as this and it is often very 
difficult, if not impossible, to obtain its true value. As a result 
several incorrect volumetric efficiencies easily obtainable from 
a card are often used in practice. 

True Volumetric Efficiency. 

(b) An ideal compressor should receive a charge equal to its 
total piston displacement and this charge should have atmos- 
pheric temperature and pressure. The weight of this charge 
would then be 

Va 

in which Vs = piston displacement in cubic feet, and 

Va = volume occupied by one pound of air under 
atmospheric conditions. 



COMPRESSED AIR 723 

If, in any case, the weight of air actually received per suction 
stroke is W , the true volumetric efficiency is 

VEf, = W'/W ...... (533) 

VaW 

= -t7 — (533a) 



(c) To evaluate this efficiency it is necessary to determine W 
and this is generally very difficult to accomplish in any real 
case. It can be done by measuring the air actually received or 
discharged in a given time and then dividing this by the number 
of suction strokes occurring during that time period ; but the 
accurate measurement of large quantities of air is generally 
difficult and therefore the true volumetric efficiency is seldom 
determined. 

Atmospheric Volumetric Efficiency. 

(d) In Fig. 467 is given in exaggerated form a real compressor 
diagram with the atmospheric line added. If there is no change 
of temperature of the working substance during charging and 
if the expansion of the clearance air 
and the compression of the mixture 
both follow the same law, the distance 
ef must measure the volume occupied 
by the clearance air, and fg is that 
occupied by the charge when compres- 
sion has progressed up to the point g. volume 

If it be further assumed that the ^^' ^ '^' 

drop of temperature from / to a' and the rise from b' to g are 
negligible, it may be said that the distance /g is a measure of the 
volume occupied by the charge when at atmospheric pressure 
and temperature. Then the volumetric efficiency, on an atmos- 
pheric line basis, would be 

„„j, distance /g , . 

VEfa = TF-^- (534) 

' a 

(e) This formula will probably give an incorrect result in all 
cases, because none of the assumptions made in its derivation 
are strictly correct. However, the error is generally not great 
in magnitude, hence, because of the simplicity of the method, 
the formula is commonly used in practice. 



724 HEAT-POWER ENGINEERING 

Suction Line Volumetric Efficiency. 

(f) A still less perfect formula is often used for determining 
the volumetric efficiency from the diagram. The point a', Fig. 
467, is first determined by continuing the straight part of the suc- 
tion line backward to intersect the expansion line. The distance 
a'b' is then taken as the volume occupied by the charge and 
the distance from a' to the zero of volumes is taken as that of 
the clearance air at the same pressure and temperature. Neg- 
lecting the fact that the suction line is below atmospheric pres- 
sure the volumetric efficiency on a suction line basis is defined as 

T.^^ distance a'b' , , 

y^u = — y^ — (535) 

(g) This method contains practically all the errors of that 
previously given with the added disadvantage of neglecting the 
difference of pressure, consequently it should never be used 
when the position of the atmospheric line can be obtained. 

344. Cooling During Compression, (a) It has been shown 
in preceding sections that isothermal compression should, in 
general, prove more economical than adiabatic. It is practically 
impossible to attain isothermal compression in any real machine, 
but it can be more or less closely approximated and generally 
without involving excessive cost. 

(b) If a compressor fitted with a metal cylinder is operated 
very slowly, i.e., one or two cycles per minute, the heat gener- 
ated by compression will be conducted away by the cylinder 
metal almost as fast as generated and in such case the com- 
pression could be made to approach an isothermal process as 
closely as desired, but it would involve the use of enormously 
large machines because of the slow operation. Some method 
must therefore be used which permits of operation at the highest 
desirable speeds. 

(c) If any form of external cooling, such as radiation consid- 
ered above, is to be used the proportions of the cylinder are 
important. That cylinder which exposes the greatest surface 
to the external cooling agent, per cubic foot enclosed, will be 
the best so far as cooling is concerned. This would indicate 
the use of cylinders of small diameter and great length, i.e., 
"long stroke compressors," but such machines are always more 



COMPRESSED AIR 725 

expensive than short stroke mechanisms, consequently a com- 
mercial limit is set to cylinder proportions adopted. 

(d) In practice a few types of compressors are cooled by radia- 
tion to the atmosphere, as, for instance, those used on locomotives 
for operating the air brakes. They are all comparatively small, 
are generally operated in strong currents of air and are at best 
rather inefhcient. It is doubtful if the compression is appre- 
ciably better than adiabatic, the radiation serving simply to 
prevent overheating of the entire mechanism by storage of heat 
from cycle to cycle. 

(e) Most commercial machines are water cooled. There are 
three distinct methods of applying cooling water, two or more 
of which may be, and generally are, used on the same machine. 
They are: — (i) Injecting water into the cylinders; (2) water 
jacketing the cylinders; and (3) compressing in stages and 
using water jacketed vessels, called "intercoolers," between 
cylinders. 

Water Injection. 

(f) The injection of water into the compression cylinder has 
been rather extensively used in Europe but not in this country. 
If the water is introduced as a solid stream but little cooling 
is effected, the compression curve approximating the equation 
pyi.sb ^Q pyi.37 = constant; but with a very fine spray the 
cooling effect is much greater, and values of the exponent n as 
low as 1.26 to 1.28 may be obtained. 

(g) The introduction of water into the cylinder has the fol- 
lowing disadvantages: — It generally increases the wear of cyl- 
inder and piston; the feeding devices are an almost constant 
source of trouble; and the air leaves the cylinder practically 
saturated with water, some of which precipitates when cooled 
in the receiver, but much remains in the air and later may cause 
trouble by freezing when the air is expanded in doing work. 

Water Jacketing. 

(h) Jacketing the compressor cylinders with water does not 
introduce the dif^culties considered above, but it is generally 
less efficient than water spraying unless it is very perfectly 
carried out. Values of the exponent n about equal to 1.25 to 
1.28 are generally attainable. 



726 



HEAT-POWER ENGINEERING 



Multistage Compression and Intercooling. 

(i) The raising of pressure from atmospheric to the desired 
receiver pressure need not occur entirely in one cylinder. The 
compression may be divided between as many cylinders as desired 
without changing the ideal process in any way. This is shown 
in Fig. 468 for the ideal case with three cylinders, i.e., compres- 
sion in three stages. It can be seen from the diagram that it 
is immaterial whether : — 

(i) Compression is carried out in one cylinder receiving the 
charge Vb and compressing it isothermally and discharging at a 
pressure P2; or 

(2) It is carried out in several cylinders, the first receiving 
a charge Vb at pressure Pi, compressing isothermally to / and 



d 


P2 


c 


V 


\f 




h 




\ 




e 






\ 










Pi 


V 




a 




Volume 

Fig. 468. 



Fig. 469. 



then discharging along /e to a second cylinder which, receiving its 
charge along ef, compresses to g, and so on until the last cylinder 
compresses to and discharges at P2. 

(j) This method has the practical advantage of making it 
possible to use what is known as "intercooling" ; for the air dis- 
charged from one cylinder may be passed through a very effi- 
cient cooler on its way to the second, and so on. The practical 
advantage of this is shown in Fig. 469, which indicates the com- 
pression line which is thus made possible. 

The line be represents ideal or isothermal compression, be' 
shows an adiabatic, and the broken line befghe" the compression 
line which might be obtained with a jacketed, or spray cooled, 
multistage compressor fitted with intercoolers. 

The compression in the first cylinder brings the material to e 



COMPRESSED AIR 727 

with a temperature higher than it had at b. An effective inter- 
cooler through which the air passes on its way to the next cyl- 
inder can reduce its temperature to the original value, so that 
compression in the second cylinder starts under the same con- 
ditions as though the process in the first had been isothermal. 

The work done in excess of that required in the ideal case is 
evidently measured by the small areas chc" , hfg and fbe, while 
without intercooling the loss would probably have been some- 
thing like that shown by the area cbc"\ 

(k) The fact that the cooling water is often below the average 
atmospheric temperature suggests the possibility of cooling in the 
intercoolers to a value lower than that on 
the isothermal. This would give a com- 
pression line similar to that shown in Fig. 
470 by befghc", which is sometimes approx- 
imated in practice when very cold water is 
available. Comparing this with the iso- 
thermal be shows that the latter may under 
these circumstances be very closely approx- 
imated. Some few machines have been 
operated with such effective intercooling 
that the sum of the work areas under the ^^' ^'^°' 

real compression lines in the several cylinders was less than 
under the ideal isothermal between the initial and final pres- 
sures. 

(1) Dividing the compression up into several stages and inter- 
cooling has a markedly beneficial effect upon the volumetric 
efficiency of a compressor for two reasons : — 

First, since the temperature range in the low-pressure cylinder 
(ist stage) is reduced, the air is heated less during the suction 
stroke, hence greater actual weight will enter the cylinder than 
would be the case in a single cylinder operating between the ex- 
treme pressure limits. 

Second, less weight of air remains in the clearance of the low- 
pressure cylinder because the discharge pressure from that cylin- 
der is lower than with a single-stage compressor, which would be 
of the same size and have the same clearance volume. 

This will be made clear by Fig. 471 in which the idealized 
cards of a three-stage compressor with clearance are abed, a'b'c'd' 
and a"b"c"d". It will be observed that the expansion of the 




728 



HEAT-POWER ENGINEERING 



clearance air in the low-pressure cylinder theoretically decreases 
the charge volume by the small amount equal to Va — Vd] whereas 
if the compression had all been carried out in this one cylinder 
the clearance air at pressure P2 would have expanded from a 
volume Ve to a volume Vf, theoretically decreasing the charge by 
the very large amount Vf — Vd- This serious loss is one worth 
preventing, if commercially feasible. 

(m) It is obvious from the diagrams and preceding paragraphs 
that the larger the total pressure range, the greater in every way 
will be the advantages of multistage compression. It thus 
happens in practice that machines for compressing to 25 or 50 
pounds per square inch are generally built single stage, while 





Fig. 471. 



Fig. 472 



those intended to compress to 100 or 150 pounds are generally 
made two-stage. Where exceptional efficiency is desired, or 
where extremely high pressures are to be attained, three-, and 
even four-, stage machines are sometimes used. 

(n) The differences between the actual cards and the ideal 
ones of each cylinder of a multistage compressor are similar to 
those which have been discussed for the single-stage compressor. 
When superposed they look something like Fig. 472, in which 
the atmospheric, intercooler, and receiver pressures are indi- 
cated by horizontal dash lines. In each case the air is drawn 
into a cylinder at a pressure below that at which it exists out- 
side of the cylinder and is discharged at a pressure higher than 
that maintained in the vessel receiving the air. This results in 
an overlapping of the cards in the center of the diagram giving 
two loops, A and B, which very evidently represent lost work. 



COMPRESSED AIR 729 

(0) The better the action of the valves and the larger the 
passages through ports, intercooler, pipes and such, the smaller 
will the areas of these loops become, the upper and lower lines 
tending to become coincident. In very well-designed compres- 
sors this lost work is so small as to be almost if not quite inde- 
terminate. 

345. Blowing Engines. Blowing engines, or blowers, are simi- 
lar to air compressors in principle, but they are generally built to 
handle relatively very large quantities of air at comparatively 
low pressures, say 10 to 20 pounds per square inch above atmos- 
phere. Comparatively little attention need be given to cooling 
under such conditions because the pressure is so low that very 
little work can be saved by such means. Moreover, the com- 
pressed air is generally heated before being used, so that any cool- 
ing during compression would call for an expenditure of heat to 
raise the temperature immediately afterward. 

Because of the large volumes of air to be handled considerable 
difificulty is generally met in designing efficient valves, particu- 
larly if operated at high speeds. As a result there are many 
different types of both inlet and discharge valves in use, some 
operating automatically under the action of springs and air 
pressure, some mechanically operated, and some partly automati- 
cally and partly mechanically operated. 

346. Turbine Compressors. Since the successful commer- 
cialization of the steam turbine, engineers have been trying to 
develop satisfactory "Turbo Compressors" or "Turbo Blow- 
ers." These compressors have a number of stages arranged in 
series, each impeller receiving its supply of air from the preced- 
ing stage and discharging into the one which follows, no valves 
being used. The stages are water cooled and iniercoolers are em- 
ployed. These machines are just beginning to assume prominence 
for compressing to pressures from 10 to 20 pounds or more per 
square inch, but as yet few have been used in this country. 

347. Compressed-air Engines, (a) Compressed air is used 
commercially in many different ways but most widely in engines 
for the production of power, the air serving as the working sub- 
stance. At first sight it seems an uneconomical method of 
producing power as the air compressor must be driven by an 



730 HEAT-POWER ENGINEERING 

engine of some sort which apparently might better be used 
directly to produce the power desired, rather than to suffer the 
additional losses incurred during compression and utilization 
of the compressed air in a second engine. 

(b) Such reasoning is generally sound for conditions where the 
desired power can be conveniently generated at the point of utili- 
zation by any of the prime movers previously considered. There 
are, however, many cases where this cannot be done. Where a 
number of small engines are to be operated at widely scattered 
points and where electrical transmission is not suitable, com- 
pressed air engines find a field to which they are admirably suited. 
Compressed air can be transmitted for great distances without 
appreciable loss, and, as will be shown later, any loss can be more 
than made good at the point of consumption. Steam, on the 
other hand, cannot be efhciently transmitted over great distance 
because of the resulting condensation; and more than this, steam 
engines of small size are very inefficient and the high temper- 
ature at which they operate renders them unsuitable when han- 
dling is required. The working substance of internal combustion 
engines can be transmitted as easily, if not more easily, than 
compressed air, but the complicated valve and ignition mecha- 
nisms, the high temperature and the hot noxious exhaust gases 
make them less desirable than compressed air engines for a num- 
ber of purposes. 

(c) Thus compressed air engines are widely used in mining 
and quarrying operations and for the driving of small portable 
tools in shops and such. In Paris there is installed a central 
compressor station which distributes compressed air, much as 
gas is distributed in this country, and air is used by the con- 
sumers for operating small plants much as electricity is used 
here. 

348. Compressed Air Engine Cycles, (a) Compressed air is 
sometimes used in engines without expansion, that is, according 
to the rectangular cycle. The work done per cycle in an engine 
without clearance is obviously 

work= V,{P2- Pi) (536) 

in which Vb is the volume displaced per stroke, P2 is the upper 
pressure, and Pi that of discharge. 



COMPRESSED AIR 731 

Such use of compressed air is very uneconomical as no use is 
made of its associated heat and, as a result, better methods of 
utilization have been devised. 

(b) A cycle similar to the Clausius described under vapor 
cycles is generally considered to represent the ideal cycle for 
air. As shown in Fig. 463, it consists of two constant pressure 
lines, dc and ba, a constant volume line ad, and an adiabatic 
expansion line cb. The theoretical work made available by such 
a cycle can easily be determined from the formulas previously 
given. 

(c) In practice the air generally enters an engine at about 
atmospheric temperature and during the approximately adiabatic 
expansion it becomes cooled, in some cases to such an extent that 
the moisture in it freezes and leads to difficulties. The theoreti- 
cal temperature decrease can never be attained in any real engine 
because heat will be supplied to the engine cylinder from the sur- 
rounding atmosphere and will tend to make the expansion more 
nearly isothermal. If the engine were operated very slowly the 
expansion would very closely approach a true isothermal. 

(d) This approach toward isothermal expansion is advan- 
tageous for the following reasons: 

(i) It tends to prevent the deposition, in the form of ice, of 
the moisture accompanying the air, thus tending to prevent the 
resultant troubles with lubrication and stoppage of valves and 
passages. 

(2) It increases the work made available, as the area under 
an isothermal is greater than that under the steeper adiabatic 
between the same two pressures. 

(3) It lessens the range of temperature within the cylinder so 
that there is less tendency to cool down the entering air. Such 
cooling would result in a decrease of volume and therefore an 
increase in the weight required per cycle. 

(e) It is interesting to note that from the theoretical view- 
point isothermal operation is not as advantageous as adiabatic. 
The object of using expansion is to make use of some of the heat 
associated with the working substance as it enters the engine. 
If the expansion is isothermal no work can be done at the expense 
of such associated heat; on the contrary, heat equivalent in 
quantity to the work done must be supplied from an external 
source. With an adiabatic expansion, however, all work would 



732 HEAT-POWER ENGINEERING 

be done at the expense of heat already associated with the gas 
as it enters the cyUnder. 

The discrepancy between theory and practice is due to the 
fact that in the assumed case heat suppHed from the atmosphere 
during the isothermal expansion costs nothing and may there- 
fore be freely used without decreasing the commercial efhciency 
of the process. 

(f) It was shown that it was uneconomical to use complete 
expansion in a reciprocating steam engine. The same thing is 
true in the case of a reciprocating compressed air engine, and as 
a result the toe of the card is cut off in practice. 

(g) Real engines are further found to operate more quietly, 
and therefore more satisfactorily, when the exhaust valve closes 
before the end of the stroke trapping some air which is then 
compressed into the clearance. Such operation causes a loss of 
diagram area and therefore a loss of work from a given size of 
cylinder running at a given speed. It may, however, result in a 
saving in the amount of air used per horse power in two ways: 

(i) When compression is not used the air admitted must first 
be mixed with that in the clearance until the full admission pres- 
sure is attained ; after that the entering air becomes available for 
driving out the piston, and 

(2) Compression tends to raise the temperature of the walls, 
cylinder head and piston and thus to decrease the cooling effect 
upon the incoming air. 

349. Preheating, (a) In practical use, compressed air en- 
gines and the compressors supplying the working fluid are gen- 
erally widely separated. It has already been shown that so far 
as the compressor is concerned the cooler the air the better. A 
cool supply means larger capacity for a given machine and 
efficient, cooling during operation means a smaller amount of 
work required. The same thing is true for the "receiver" or 
storage tank, and for the pipe line carrying the air to the engine, 
for the cooler the air the smaller can these parts be for a given 
quantity of air. 

(b) Conditions are, however, quite different so far as the 
engine is concerned. The warmer the air, within reason, the 
better. 

If the compressed air could be heated at constant pressure 



COMPRESSED AIR 733 

before entering the engine, it would expand according to Charles' 
law. A given volume of heated air admitted to the engine would 
represent a smaller actual weight but would be able to deliver 
the same amount of work as a larger weight of colder air, and 
there would be the added advantage that there would be less 
danger of the moisture freezing at the end of expansion. 

(c) Such heating of the air is known as " preheating " and 
the devices in which it is effected are called "preheaters." It 
is actually used in places where the transmission piping is of 
great length and also where the engine units are few and of large 
size. It is found in practice that the running expense for the 
fuel supplied for preheating is less than the extra charges against 
the larger compressor and pipe line which would otherwise be 
used. 



CHAPTER XLII. 
REFRIGERATION. 

350. Definition, (a) By refrigeration is generally meant the 
removal of heat from a body, or substance, to such an extent as 
to leave it, or maintain it, at a lower temperature than that of 
its surroundings. This may be done commercially in moderate 
climates by the use of ice ; it may be accomplished in the labora- 
tory by the use of liquefied gases; it may be done in very hot 
climates by the naturally rapid evaporation of water. 

(b) In the ordinary engineering application of the term, how- 
ever, it is taken to mean the removal of heat by mechanisms, 
or systems, which will be described in later sections and which 
are grouped under the title of Mechanical Refrigeration. 

351. Thermodynamics of Refrigeration, (a) It was shown 
in Sect. 49 (h) that by the expenditure of energy (A£) a reversed 
I -p I heat engine would remove heat from a body 
I ' I at low temperature and would discharge to 

t <-AQi=AQo+AE another body, at higher temperature, that 

heat plus the heat equivalent to the energy 

j; expended in the operation. That is, a re- 

V ; \'~j^ — versed heat engine shown diagrammatically 

j4t1^ as R in Fig. 473 can receive a stream of heat 

\ \\ J ^ LQi from the low temperature body T^ and 

discharge the larger stream A(2i, made up of 

' ^ . ' A (22 and AE, to the high temperature body Ti. 

^^' ^'^^' (b) This is a process of refrigeration because 

heat can be removed from the low temperature body even if its 

temperature be far below that of its surroundings. It thus 

appears that the reversed heat engine, which has been called 

a heat pump, is what may now be called a refrigerator, or 

refrigerating machine. 

(c) Imagine the Carnot cycle, shown in Figs. 18 and 21 to 
PV- and T(/)-co6rdinates, to be carried through in the direction 

734 



REFRIGERA TION 735 

dcha for purposes of refrigeration. Heat will be absorbed along 
the line dc at temperature T2, and in quantity as shown on the 
T0-diagram by the area dcef. The work expended in driving the 
machine will be shown by the area ahcd on the PV-diagram, if 
measured in foot-pounds, or by the similarly lettered area on the 
T0-diagram, if measured in thermal units. Heat will be dis- 
charged along the line ha at temperature Ti and its quantity 
will be the area, feba on the T^-diagram, equal to the sum of two 
areas previously considered. 

(d) The expenditure made in order to abstract the heat AQ2, 
shown in Fig. 21 by area dcef, is obviously the energy A£ used 
in driving the machine as shown by the area abed. If the heat 
removed, AQ2, be taken as the result obtained, the efficiency of 
the process is ^^ ^^^^^^ ^^^ 



Ef 



Expenditure A.E 



(e) It is obvious from the T^-diagram of Fig. 21 that for the 
case for which this figure was drawn AQ2 is considerably greater 
than AE, hence the ratio which has just been given as the effi- 
ciency will be greater than unity. This is a very common 
property of refrigerating processes. Since engineers are not ac- 
customed to speak or think of efficiencies greater than unity it 
is common practice to call this ratio the Coeffieient of Performance 
(Co. P.), or the Figure of Merit, rather than the efficiency of the 
process. Then the 

C.o.P.=f| .■ (537) 

for refrigerating machinery of this kind. 

(f) The apparently remarkable attainment of an efficiency 
greater than unity is meaningless. The work expended and 
the heat removed from the cold body are really not connected 
in any such way as are heat supplied and work done in the case 
of an engine. This can best be seen from the T^-diagram of 
Fig. 21. Assume the line dc to be moved upward while the 
line ab maintains its- position. Then the heat removed {AQ2) 
will obviously increase while the area of the cycle, representing 
AE, will decrease, that is, it takes less work to remove larger 
amounts of heat. 

(g) That this should be so can easily be seen by carrying the 



736 HEAT-POWER ENGINEERING 

assumptions to the limit. If dc rises above ab the previously 
cold body has attained a temperature greater than the previ- 
ously hotter one and work can actually be obtained by allowing 
heat to flow from it to the latter. Obviously the coincidence of 
the lines dc and ah would indicate that the two bodies are at 
the same temperature, that no work is attainable by heat flow, 
and that no work is necessary to cause heat flow. 

Requirements for Maximum Coefficient of Performance. 

(h) Inspection of the T0-diagram will show that anything 
which brings the two lines ab and dc, that is, the temperatures 
Ti and T2, closer together will increase the value of the coeffl- 
cient of performance. This can be done by dropping Ti or by 
raising T^. Dropping Tx will decrease A£ but will not change 
A (22- Raising T^ will decrease A£ and increase A (22 by the 
same amount. It is therefore evident that raising the lower 
temperature is more effective for attaining a high coefficient 
than lowering the upper temperature; but this results in a 
higher temperature in the cold body and hence may not be 
desirable. 

Obviously with given upper temperature Ti, the lower the tem- 
perature {T2) of the cold body is maintained the smaller will be 
the Co. P.; and, with given lower temperature {T2), the lower 
the temperature of the hot body receiving the heat, the larger 
will be the value of the Co. P. 

Theoretical Values of Coefficient of Performance. 

(i) For purposes of comparison with real refrigerating ma- 
chinery the ideal reversible refrigerator already described is 
very useful although its theoretical performance can never be 
even closely approximated by a real machine. The case is 
very similar to that of engines where the perfect Carnot 
engine is used as a measure of perfection although practically 
unattainable. 

(j) In order that numerical comparisons may be made later, 
several values of the coefficient of performance will now be 
obtained for a Carnot cycle refrigerator. The formula pre- 
viously given can be put in more convenient form for this pur- 



REFRIGERATION 



737 



pose in the following way. It was shown on page 82 that for a 
Carnot engine the net work is 

AE = RTi loge r - RT2 loge r 
= (ri- T2)Rloger, 
and that AQz = RT2 log^ r. 

Then, for this case, 

AQ2 _ RT2 logeT ^ T2 

A£ (Ti-T2)R\oger Ti - T^' ' 



C.o.P. 



(538) 



Values of the C.o.P. can be easily obtained by substitution of 
assumed temperatures in the last term. 

A very common case would be a machine which theoretically 
withdrew heat from a cold body at 18° F. and discharged it to 









/ 








/ 






>f/ 


/ 




^ 


^ 

^ 


p^ 


^^ 


^ — 


rrlfe 


lOO^F^^ 



10 20 30 40 

Temperature, \ in ^ah. IDegrees 
Fig. 474. 

a hot body (cooling water) at a temperature of, say, 50° F. 
coefficient of performance in this case would be 

AQa ^ T2 18 + 460 

AE~ T,-T2~ (50 + 460) - (18 + 460) 



The 



= 15, approx. 



(k) The results obtained by varying the two temperatures 
are shown by the curves in Fig. 474, in which each curve is 
drawn for a certain upper temperature Ti and shows by its 
rise toward the right the increase in the value of the coefificient 
of performance with rise of the temperature T2. 



738 



HEAT-POWER ENGINEERING 



352. The Air Refrigerating Machine, (a) Any gas, not lique- 
fiable at ordinary temperatures, may be used as the working 
substance, or refrigerant, in commercial refrigerating machines, 
but air is the gas most commonly used. This material has the 
advantages of being readily procurable, non-poisonous and can 
be brought into actual contact with food stuffs and such, which 
are to be cooled or kept cool without detriment to the latter. 

(b) In the ideal machine the same charge of air would be used 
continuously and the entire operation would be carried out in 
a single cylinder. In practice it is found more convenient to 

use separate organs to perform 
different functions during the 
cycle and it is generally found 
best to discharge the air used 
in each cycle and to draw in a 
fresh supply for the next. It 
will be noted that this parallels 
the conditions met with in most 
real engines. 

(c) An idealized refrigerating 
machine using a unit weight of 
air as a working substance is 
shown diagrammatically in Fig. 475, the apparatus consisting of 
a compression cylinder, an air cooler and an expansion cylinder. 
The compression cylinder (without clearance) draws cold air 
from the cold-storage room at atmospheric pressure and at 
a constant temperature T2, according to 
the constant pressure line ab in Fig. 476. 
The air is then compressed adiabatically, 
as shown by be, and discharged at the 
higher pressure Pi with a temperature Ti, 
higher than T2, and specific volume dc. 
If the delivery pressure is sufficiently 
high, the temperature attained may be 
greater than that of available cooling 
water so that the air may be cooled by 
discharging it into the cooler through which this water is circu- 
lated. By assuming the volume of the cooler to be very large, 
the reduction of temperature may be assumed, without sensible 
error, to take place at constant pressure; hence, the delivery to 




Fig. 475- 




Fig. 476. 



REFRIGERATION 739 

the cooler is shown by the Une cd in the figure, but when cooled 
the volume of the air is de at this same pressure. 

Continued operation of the compressor cylinder would result 
in continued duplication of the cycle abed. 

(d) The expansion cylinder running at the same speed as the 
compressor can be imagined as receiving from the cooler exactly 
the same weight of air per cycle as is delivered by the com- 
pressor. This air will be admitted according to the constant- 
pressure line de, in Fig. 476, and its adiabatic expansion will be 
according to line ef, bringing the material back to the initial 
pressure P2 but with a temperature lower than the original 
temperature 7*2, for, according to Charles' law, 

Tf/T, = Tf/T, = Vf/V,, 

from which Tf=T2{Vf/Vb) (539) 

This cooled air at temperature Tf can then be discharged to 
the cold-storage room to balance heat leaking into it through 
the walls or brought in by fresh produce. It is only necessary 
to properly regulate the quantity of air handled and the tem- 
perature at which it is returned, to maintain any desired tem- 
perature (within limits) in the cold-storage room. 

Power Required. 

(e) The work consumed by the compressor is obviously shown 
by the area abed and that made available in the expansion 
cylinder is similarly shown by the area defa. The net work 
required per cycle is then only fbee if the expansion and com- 
pressor pistons be connected together. This work can be ex- 
pressed in terms of temperatures, pressures and volumes by the 
equations given in Chap. VIII. 

Refrigerating Effect and Coefficient of Performance. 

(f) The net refrigerating effect, that is, the heat AQ2 removed 

from the cold room per cycle, is obviously the difference between 

the heat in the air as it leaves and that in the same air when it 

returns. That is, a^ -rj//- ^t- t ^ /■^.^\ 

AQ2 = WCpiTb- Tf), (540) 

in which . 

W = weight of air per cycle, 

Cp = specific heat of air at constant pressure, 

Th = temperature of air leaving cold room, and 

Tf — temperature of air returning to cold room. 



740 HEAT-POWER ENGINEERING 

(g) In a similar way the heat rejected to the water must be 

AQ,= WCATc-Te). (541) 

Since \E = AQi - AQ^, it follows that 

AE = WC, (n - Te) - WC, (n - Ty), . (542) 
and from these values 

^•"■^- A£ wCp (n - Te) - ^Cp (n - r^) 

Th — Tf , . 

• • • • (543) 



This value may be further simplified as follows: Inverting 
both sides of the equation gives 

1 . _ (n - Te) 
c.o.p. n - T/ 

and since from the adiabatic relation 

T\ Te Tr. - Te 

n 

_l 

C.o.p. 

Co.?. = .=^-^V - -^r^^ .... (544) 



and 



Tf n - Tf 

Tc-n ^ Te- Tf 

n Tf 

n Tf 

T. - n T.- T, 



Comparison with the Reversed Carnot Cycle. 

(h) A Carnot cycle refrigeration would work between the 
temperatures Tb, which is the highest temperature of the cool 
material, and Te, which is the lowest temperature of the warm 
material. Its coefficient of performance would therefore be 



C.O.P. 



Te 



Since {Te — T^) is less than {To — T^) in Eq. (544), it follows 
that even in the ideal case the real refrigerating machine de- 
scribed must have a lower coefficient of performance than that 
obtained with the reversed Carnot cycle. 

The difference is due to the use of two irreversible, variable- 
temperature, constant-pressure processes which in the real case 
increase the temperature range. The temperature of the air 



REFRIGERA TION 74 1 

discharged to the cooler must be so high that the water used 
can remove heat from it, finally bringing the air down to a value 
approaching that which it had when entering the compressor 
cylinder. 

Similarly, the air is cooled during expansion to a temperature 
considerably lower than that of the cold room, and when intro- 
duced into that room it is heated irreversibly until it finally 
attains the temperature existing there. 

Practical Modifications. 

(i) In a real machine operating on the cycle just discussed, 
there will be clearance and valve losses in both cylinders, fric- 
tion throughout the mechanism, and heat losses to and from the 
working substance as it passes through the apparatus with 
temperatures different from those of surrounding bodies. These 
will all increase the size of machine and the amount of work 
necessary to produce a given amount of refrigeration. 

(j) In practice it is customary to water jacket the compressor. 
This makes the compression line less steep, i.e., intermediate 
between the adiabatic and the isothermal, and proportionally 
reduces the amount of work required. It also leaves less heat 
to be removed in the cooler and makes possible the use of a 
smaller vessel for that purpose. It is therefore decidedly ad- 
vantageous. 

Actual Coefficient of Performance. 

(k) Both in the ideal and actual cases, the coefficient of per- 
formance of air refrigerating machines is very poor in compari- 
son with machines using vapors such as ammonia. The use of 
air machines is therefore dictated by convenience rather than by 
economy of power. 

For average cold-storage conditions, in temperate climates 
for instance, the coefficient of performance of a Carnot cycle 
refrigerator is about 9 to 10. The coefficient of the ideal air 
machine (Eq. (544)) is only about 1.5 to 2 ; and in the real machine 
it is generally, if not always, below 0.75, as determined by test. 

353. Vapor Compression Process of Refrigeration, (a) It 

was shown in the previous section that the air machine there 
described was considerably handicapped by the cycle on which 



742 HEAT-POWER ENGINEERING 

it operated, its theoretical coefficient of performance being 
necessarily much lower than that of the ideal Carnot cycle 
refrigerator because the constant pressure reception and rejec- 
tion of the heat are not reversible processes with gases. 

(b) By using a liquid and its vapor as the working substance, 
instead of a gas, a much better performance can be obtained 
because the constant-pressure processes for saturated vapors 
and their liquids are reversible isothermal ones. It therefore 
follows that with such working substances the same sort of 
machine as that just described would in the ideal case operate' 
on a Carnot cycle which would give the best performance 
possible. 

(c) Fig. 477 can be used for the purpose of developing this 
cycle by assuming the discharge pipe of the expansion cylinder 

and the inlet pipe of the compressor con- 
nected by a coii, as shown dotted by C 
in Fig. 475, so that the entire system is 
"closed." This coil may be regarded as 
immersed in the material to be cooled. 

Imagine the ideal compression cylinder 

to draw in a charge of mixed saturated 

vapor and its liquid, at temperature T^ 

jrj ^ from this coil, as shown by the line ah 

in Fig. 477. The return stroke of the 

piston will result in adiabatic compression to the point c, and, 

with a properly chosen quality at h, the material can be brought 

to the condition of dry saturation at c. 

From c to d the working substance is driven into the cooler 
which now acts as a condenser reducing all of the vapor to the 
liquid form with volume de. The liquid may then be admitted 
to the expansion cylinder, as shown by the line de, expanded 
adiabatically to / and discharged along the line fa into the 
assumed coil C, where it may be vaporized wholly, or partly, 
at temperature T2, at the expense of heat in the material 
surrounding the coil. After this it may be readmitted to the 
compressor and the cycle repeated. 

(d) So far as cycle is concerned the operations outlined have 
resulted in the generation of the reversed Carnot cycle fhce. 
So far as heat is concerned they have resulted in the removal of 
heat A (22 from the cooler substance during vaporization at tern- 




REFRIGERATION 743 

perature T-^ and in the surrender of a larger amount of heat A(2i 
to the warmer substance (condensing water) at the tempera- 
ture Ti. 

T<|)-Diagram of Vapor Process. 

(e) The T</)-changes of ammonia vapor and its Hquid, in an 
ideal case, are shown in Fig. 478 in which points are lettered to 
correspond with those of Fig. 477. The liquid line and the 
saturation line have been added to the diagram. 

From this diagram it can be seen that 
the heat absorbed from the cooler body 
is ^2 {xh — Xf) and that discharged to the 
warmer body is ri. The work required in 
B.t.u. per pound of substance is therefore 







c 


; 






/ 

/ 
/ 




\ 

\ 
\ 


/ ^ 7' 




Entropy 





AE = ri- r2 {xj, - Xf). . (545) 

Fig. 478. 

The mixture of liquid and vapor is 

cooled during the expansion ej by the giving up of heat to cause 

partial vaporization as indicated. 

Practical Modifications of Vapor Compression Process. 

(f) In any real case the expansion cylinder would be very 
small in comparison with the compression cylinder, and the 
work done by it would be practically negligible. It has come 
to be regarded as more of an incumbrance than a benefit and is 
commonly omitted in real machines. In its place is substi- 
tuted an " expansion valve,'" as X in Fig. 479. This is merely a 
throttle valve through which the working substance can flow 
from the high pressure of the condenser to the low pressure of 
the coil. 

(g) This flow is an adiabiatic process but is not reversible and 
hence is not isentropic. It is not represented by the line ej of 
Fig. 478, but by some line starting at e and terminating on the 
line Jb at some point /' to the right of /. The entropy increases 
and the possible refrigeration effect decreases because the energy 
which would have been given up as external work during isen- 
tropic expansion here remains associated with the substance giv- 
ing it the higher quality x/ , instead of Xf. The heat which can 
be absorbed from the body to be cooled is then only r^ (xb—x/) 
instead of r^ {xh — Xf). 



744 



HEAT-POWER ENGINEERING 



In real cases the difference is so small that it is negligible in 
comparison with the increase in mechanical efficiency and ease 




AVa'te r Ont 



= Compression 



Cold Storage Room 



Fig. 479- 

of Operation, and with the decrease in first cost and operating 
expense. 

Actual Coefficient of Performance. 

(h) The great majority of vapor compression machines oper- 
ate with ammonia vapor for their working substance. Such 
machines give a coefficient of performance of from 5 to 7 under 
conditions which give a coefficient of 9 to 10 for the ideal Carnot 
cycle. In comparison with the values given for air machines 
these performances are very much higher and it is doubtful if 
the ammonia machines can be greatly improved. 

354. Relative Advantages of Different Vapors, (a) While 
most vapor refrigerating machines use ammonia this material 
is not the only one available. For plants used aboard ship 
carbon dioxide is often preferred and many stationary machines 
have been operated with this substance and with sulphur di- 
oxide. Other materials, including water, have been used. 

(b) The choice of ammonia as the common working substance 
is decided largely by practical considerations, though it so hap- 
pens that certain thermodynamic properties would lead to the 
same choice. The most important considerations are probably 
those of volume and pressure. 



REFRIGERATION 745 

(c) The actual volume of working substance required to cause 
a given amount of refrigeration determines the size of machine 
required. The larger the machine, the greater the friction 
losses if other things are equal. Since all friction must even- 
tually result in the generation of heat the refrigerating effect 
will be diminished thereby. Bulk is therefore undesirable be- 
cause of cost of machines, cost of power to operate and loss of 
refrigerating effect by friction. 

The pressure is important in two ways. Some available 
substances have vapor pressures below atmospheric when at the 
temperatures common in refrigeration. Their use would mean 
the maintenance of a vacuum within the refrigerating machine 
which is by no means a simple matter because of difficulty with 
air leakage. Other substances have vapor pressures so high 
that they can be used only with great difficulty. 

(d) Ammonia is quite satisfactory both as regards bulk and 
pressure. More than twice the bulk of sulphur dioxide is re- 
quired for the same refrigerating effect, and between 300 and 
400 times the bulk of water vapor. Carbon dioxide requires 
only about one-quarter the bulk of ammonia vapor but, as will 
be seen, is handicapped by enormously high pressures. 

The pressure of water vapor is entirely below atmospheric 
at refrigerating temperatures, while that of sulphur dioxide is 
below for the lowest temperatures and only slightly above for 
the highest temperatures. 

The pressure of ammonia vapor varies from about 20 or 25 
pounds to something below 200 pounds, while that of carbon 
dioxide varies from about 300 to 1000 pounds per square inch. 

It is obvious that the best commercial balance is struck when 
ammonia is adopted, excepting in cases where an ammonia leak 
might cause very serious difficulties. 

(e) In the case of real machines there is also another point which 
must be considered and which is more of a thermodynamic nature. 
Where an expansion valve is substituted for the expansion cylin- 
der, the working substance brings into the refrigerating coil heat 
which in the ideal case would have been converted into work and 
used in driving the machine. Obviously any heat brought into 
the coil by the working substance itself means just so much less 
heat to be abstracted from the s-urroundings to cause evapor- 
ation, hence there will be an equal reduction in the refrigeration. 



746 HEAT-POWER ENGINEERING 

That material which brings in relatively the smallest amount 
of heat in this way will be the most desirable if other things 
are equal. 

The amount of heat under consideration is that in the liquid 
at the end of the liquefaction process, that is, it is the quantity 
when the working substance is at the higher temperature Ti 
which is above that in the same liquid at the lower temperature 
T2. It is therefore equal to C (Ti — T2) in which C is the specific 
heat of the liquid. The larger this value in proportion to the 
latent heat of vaporization at the temperature T2, the poorer the 
material for use in a vapor compression machine having an ex- 
pansion valve. 

From this point of view, water is the best of the materials 
cited as possibilities and ammonia comes next, carbon dioxide 
being the worst of all ; thus, ammonia forms a good commercial 
compromise. 

355. The Ammonia Absorption Process, (a) The vapor 
compression machine operates (i.e., refrigerates) because the 
process of vaporization requires a supply of heat from external 
sources and the process of liquefaction yields heat to external 
media. Any device or machine which can bring about such alter- 
nate liquefaction and vaporization can be used as a refrigerating 
machine. 

(b) The so-called absorption refrigerating machine carries 
through these two processes in a manner analogous to that of the 
compression machine but by entirely different means. It is illus- 
trated diagrammatically in Fig. 480 and operates in the following 
way: 

(c) The generator contains a strong solution of ammonia in 
water, and the ammonia is driven off from this solution at high 
temperature and pressure, by the heat supplied by the steam 
coils shown at S. The vapor, under this pressure, enters the 
condenser K in which it is liquefied, as in the previous case. It 
then passes through the expansion valve X and evaporates in 
the refrigerating coils C as before. 

Leaving the refrigerating coils as vapor, it enters the absorber 
A at low pressure and low temperature and is absorbed by water 
to form a strong solution which, by a pump P, is delivered to 
the generator to displace that which has given up ammonia 



REFRIGERATION 



747 



vapor under the action of heat, and which is then returned to 
the absorber. 

(d) The absorber, pump and generator together correspond 
to the compressor of the previous type. The action in the ab- 




Steam 
Liquor (Weak) 



Fig. 480. 

sorber corresponds to the charging operation of the compressor; 
the action of pump and generator corresponds to the compression 
and discharge. 

Coefficient of Performance of Absorption Machines. 

(e) No mechanical power, except the small amount for pump 
P, is supplied such a machine, the absorption of heat at a low 
temperature following from the supply of heat at a high tem- 
perature. The coeflficient of performance cannot therefore be 
obtained as in previous cases. If, however, it is considered as 
the quotient found by dividing the heat absorbed by heat sup- 
plied to cause that absorption, a ratio is obtained which may 
be used in the same way as the coefhcient of performance. 
Comparing such ratios with those for ideal refrigeration oper- 
ating on a reversed Carnot cycle it is found that the absorption 
machine has a coefficient of performance of about one-eighth to 
one-tenth that of the ideal. 

(f) It was shown in Sect. 353 (h) that for the compression 
process the coefficient is about seven-tenths of the ideal and it 
would seem from this that the absorption machine should give 
a very poor commercial result. It should, however, be observed 



748 HEAT-POWER ENGINEERING 

that the coefficient for the compression machine was based upon 
the energy suppHed the compressor and not upon the heat 
supphed the plant which generated that energy. 

To make the two results comparable the value of 0.7 for the 
compression machine must be multiplied by the thermal effi- 
ciency of the plant on the basis of developed horse power. 
When this is done the two types are more nearly on an equal 
footing, with the absorption machine giving the better perform- 
ance for wide temperature ranges, excepting when a very efficient 
plant is used to drive the compression machine. 

356. Rating of Refrigerating Machines, (a) Refrigerating 
machines are generally used in practice for the purpose of main- 
taining a cold atmosphere in "cold-storage rooms" or for the 
making of ice. The ammonia machines generally achieve both 
results indirectly by cooling brine and pumping the brine to the 
point at which heat is to be absorbed. 

(b) No matter what use is made of the refrigerating machine 
or how it operates, it is rated on ice-melting capacity in pounds, 
or tons, per unit of time. To melt one pound of ice at 32° F. to 
water at the same temperature requires approximately 144 B.t.u. 

A machine which could absorb from the cold body a quantity 
of heat equal to 144 B.t.u. per hour would be able to melt ice at 
the rate of one pound per hour. The capacity is generally ex- 
pressed in tons per twenty-four hours, thus this machine would 
have an ice-melting capacity of (144 X 24) -^ 2000 = 1.25 tons, 
approximately. 

Ice-melting capacity has no direct connection with ice-making 
capacity. When making ice the water from which it is made 
must first be cooled to freezing temperature, the ice then formed, 
and generally reduced to a temperature considerably below 32° F. 
As a result, the ice-making capacity of a machine is generally 
only about one-half of its ice-melting capacity. 



PROBLEMS. 



CHAPTER n. 

1. Assuming the specific heat of water constant and equal to unity, how 
many B.t.u. are required to raise the temperature of i lb. of water from 
32° F. to 212° F.? 

2. Under the same assumptions as above, how many B.t.u. must be ab- 
stracted to lower the temperature of 20 lbs. of water from 212° F. to 32° F.? 

3. If 33,000 ft. -lbs. of mechanical energy are completely converted into 
heat energy, how many B.t.u. result? 

4. If mechanical energy is made available at the rate of 33,000 ft. -lbs. per 
minute for i hour it is said that i horse-power hour, has been made available. 
What is the energy equivalent of i horse power in thermal units? 

5. Find the weight of water (specific heat = i) which will have its tem- 
perature doubled by the addition of 180 B.t.u., the final temperature being. 
120° F. 

6. Find the change of temperature of 12 oz. of lead (specific heat = 0.0314)' 
when 4 B.t.u. are added. 

7. Assuming no loss by radiation, how much electrical energy in terms of 
thermal units would be required to raise the temperature of a copper wire 
one mile long and weighing 0.3 lb. per foot through a range of 10 degrees?' 
The specific heat of copper is 0.095. 

8. If 130 B.t.u. raise the temperature of 10 lbs. of cast iron 100 degrees, what 
must be the specific heat of this material? 

9. Assume the specific heat of wrought iron as 0.113, the specific heat of 
water as i.o and the weight of water as 62.5 lbs. per cu. ft. Find the increase 
in temperature of 2 cu. ft. of water when a common temperature of 45° re- 
sults from putting into the water a piece of iron weighing 10 lbs. and at a 
temperature of 1000° F. 

10. A winch is used in lowering a load of two tons a vertical distance of 
50 ft. The load is lowered by means of a friction brake which prevents the 
attainment of too high a speed and which brings the load to rest just as it 
reaches the end of the 50-ft. drop. It takes one minute to lower the load. 
Neglecting friction of bearings and similar losses, how much heat must be 
radiated by the mechanism of the brake and winch? How many horse power 
must be absorbed by the brake? 

11. An electric motor receives electrical energy, converts part of it into 
heat within itself and delivers the remainder at the pulley as available me- 
chanical energy. A certain motor delivers, in this way, 20 horse power (i h.p. 
= 33,000 ft. -lbs. per min.) and converts into heat 15 per cent of all the energy 
supplied it. How much heat must this motor dissipate per hour? How many 
ft. -lbs. of energy must be supplied it per minute? 

12. Assume yourself called upon to investigate the claims made for a piece 
of mechanism with the following characteristics. It receives no energy of 
any kind excepting that given it by a driving belt which supplies 250,000 ft.- 
Ibs. per minute. It is clainied that the mechanism gives out or makes avail- 
able 400 B.t.u. per minute. Would you make the investigation? Why? 

13. What is the largest amount of heat energy which the mechanism oper- 
ating as in problem 12 could make available per minute in an ideal case? 
Could it do this in practice? Why? 

749 



750 HEAT-POWER ENGINEERING 

14. Assume yourself called upon to investigate the claims made for a piece 
of mechanism with the following characteristics. It is supposed to receive 
no energy of any kind excepting 300 B.t.u. per minute and is supposed to 
make available 240,000 ft. -lbs. of mechanical energy in the same time. Would 
you make the investigation? Why? 

15. Assume that the mechanism in problem 14 above is supposed to receive 
only 300 B.t.u. as before and that in the ideal case (neglecting friction, radia- 
tion, conduction and similar losses) it is supposed to deliver 233,400 ft. -lbs. 
in the same time. Would you make the investigation? Why? 

16. Assume that the value of the variable specific heat C of a subtance is 
given for temperature t by the equation 

C = 0.5 + 0.02 t. 

Find the total heat required to raise the temperature of 12 lbs. of the material 
from 50° to 100° F. 

17. An engine receiving 300 B.t.u. per minute and no other energy of any 
kind rejects to a cold body an amount of energy equal to 150 B.t.u. per 
minute. If there are no friction or similar losses, what would be the amount 
of mechanical energy in ft. -lbs. made. available per minute? 

18. If the engine operating as in the first part of prob. 17 above loses in 
friction and radiation 10. per cent of the energy which would otherwise be 
made available, what will be the amount of mechanical energy in ft. -lbs. 
made available per minute? 

19. A factory building is being designed. Calculations from the radiating 
surface of the building, character of that surface, location, direction of winds, 
etc., indicate that about 400,000 B.t.u. per hour must be liberated within the 
building to keep the temperature up to 65° F. The heating engineer desires 
to keep the cost of the heating equipment down to a low figure and believes 
that he can do so by allowing for heat generated by friction of the moving 
mechanisms within the factory. He discovers that 100 horse power (i h.p. 
= 33,000 ft.-lbs./min.) are to be continuously supplied the factory by means 
of an electric motor and that all of this power will be consumed within the 
factory. The motor has an efficiency of 85 per cent. What allowance can 
the heating engineer make on theoretical grounds? 

20. In the manufacture of a certain chemical compound it is necessary to 
stir and mix a rather heavy liquid in a large vat. If the temperature of the 
liquid rises above a certain value it is apt to cause a violent explosion. The 
formation of the compound causes the absorption of 20,000 B.t.u. per hour 
and the vat is so arranged that 25,000 B.t.u. can be carried away per hour 
under all conditions by means of a water jacket and loss to the surrounding 
atmosphere. How many foot-pounds of energy could be supplied the stirring 
apparatus per hour without causing a dangerous rise of temperature? 

CHAPTER IV. 

1. An ideal gas occupies a volume of 17 cu. ft. at a pressure of 1500 lbs. per 
sq. ft. and a temperature T. What will be its volume at a pressure of 2000 
lbs. per sq. ft. and at the same temperature? 

2. A gas has its volume halved by an increase of pressure at constant tem- 
perature. The initial pressure was 3000 lbs. per sq. ft.; what is the final 
pressure" 



3. A gas with an initial pressure of 4500 lbs. per sq. ft. is contained in a 
water-jacketed cylinder, the jacket being so connected with a water system 
that the temperature within it is always 60° F. The cylinder is fitted with a 
frictionless piston which can be moved in or out as desired. The piston is 
moved very slowly so that the gas is maintained at the same temperature as 
the water jacket. At the end of a certain time the pressure of the gas within 
the cylinder is found to be 14.7 lbs. per sq. in. Was the piston moved in or 
out? What was the amount of motion required to effect the change? 



PROBLEMS 751 

4. A balloon is filled with hydrogen gas at atmospheric pressure (14.7 lbs. 
per sq. in.) and at atmospheric temperature. The balloon then ascends to a 
point where the atmospheric pressure is only 12.7 lbs. per sq. in. but the 
temperature is the same as at the lower level. If the balloon is made of non- 
extensible material, what will be the pressure of the hydrogen gas within it? 
If the balloon is made of perfectly stretchable material (stretching with appli- 
cation of only infinitesimal forces), what will be the pressure within it? In 
the latter case what expansion of volume must have occurred? 

5. The inner tube of a certain tire has a capacity of 854 cubic inches. How 
many pounds of air will it contain when filled with air at a pressure of 70 lbs. 
per sq. in. and a temperature of 32° F.? (One cubic foot of air at 14.7 lbs. 
pressure and 32° F. weighs 0.0807 lbs.) 

6. What will be the increase of pressure of air in problem 5 if the tempera- 
ture rises to 70° F. and the tire does not stretch during the process? 

7. A closed metal tank is designed to be safe when subjected to an internal 
pressure of 100 lbs. per sq. in. It is used to hold compressed air and is filled 
with this material at a temperature of 60° F. and a pressure of 80 lbs. per sq. 
in. The tank stands in the sun and its contents may attain a temperature of 
125° F. Assuming that the tank does not expand with temperature and 
pressure changes, will the designed pressure be exceeded? What temperature 
would have to be attained to raise the pressure of the air to the 100 lbs. for 
which the tank was designed? 

8. A submarine boat is closed at the surface, with air content at a tempera- 
ture of 80° F. and a pressure of 14.5 lbs. per sq. in. After sinking beneath 
the surface the temperature of the air drops to 40° F. If the hull has not 
changed size during the temperature change what must be the pressure of the 
air under the submerged conditions? 

9. Assuming that the men and machinery in the boat of problem 8 radiate 
enough heat to maintain a temperature of 60° within the boat what will the 
air pressure be? 

10. A quantity of gas occupies a volume of 10 cu. ft. at a pressure of 5000 
lbs. per sq. ft. and a temperature of 70° F. What will its volume be at a 
pressure of 7000 lbs. per sq. ft. and a temperature of 100° F.? 

11. A quantity of gas occupies a volume of 15 cu. ft. at a pressure of 40 
lbs. per sq. ft. and a temperature of 60° F. What will be its volume at a 
temperature of 70° F. and a pressure of 30 lbs. per sq. ft.? 

12. A quantity of gas occupies a volume of 10 cu. in. at a pressure of 7000 
lbs. per sq. ft. and a temperature of 50° F. What will be its volume at at- 
mospheric pressure (14.7 lbs. per sq. in.) and a temperature of 70° F.? •' 

13. The value of R for a certain gas is 55. One pound of this gas occupies 
a volume of 12.8 cu. ft. at a pressure of 14.7 lbs. per sq. in. What is the tem- 
perature of the gas? What will be the volume of two pounds of this gas if 
pressure and temperature (ordinary Fahrenheit scale) are doubled? 

14. Three pounds of air are enclosed in a nonexpansible vessel. The pres- 
sure is 20 lbs. per sq. in. and the temperature is 80° F. The value of R is 53.34. 
What is the volume content of the vessel? What will be the pressure of the 
air if its temperature is increased to 180° F.? 

15. One-half pound of nitrogen gas is contained in a cylinder fitted with a 
piston. The temperature of the gas is 80° F. and its pressure is 40 lbs. per 
sq. in. The piston moves out until the volume of the gas has doubled and 
it is then found that its pressure is 20 lbs. per sq. in. What must the tempera- 
ture have become? (R for nitrogen = 55.16.) 

16. A certain gas is collected over mercury and measured. It is found to 
have a volume of 10 cu. in. at a pressure of 14.6 lbs. per sq. in. and a tem- 
perature of 60° F. The gas is then passed through a reagent which absorbs 
part of it and the remainder is collected over mercury and measured. It 
measures 6 cu. in. at the same pressure as before but the temperature has 
changed to 70° F. between the two measurements. What percentage of the 
original volume was absorbed by the reagent? 

17. The products of combustion from a boiler reach the base of the stack 



752 HEAT-POWER ENGINEERING 

at a temperature of 500° F. At the top of the stack their temperature is only 
200° F. Neglecting the slight pressure change which would occur during the 
ascension, determine the relative values of the cross-sectional areas at top and 
bottom of the stack to give equal gas velocities at the two points. 

18. An air compressor draws into its cylinder a charge of air at a pressure 
of 13.5 lbs. per sq. in. and a temperature of 60° F. It compresses this air to a 
volume equal to one-quarter of its original value and the pressure attained is 
60 lbs. What must be the final temperature of the air? 

19. A diving bell is to be used for executing certain work under water. It is 
made in the form of a flat-ended cylinder open at the bottom. The inside diam- 
eter is 12 ft. and the inside height is 14 ft. The men and tools accommodated 
within the bell occupy a cubical content of 120 cu. ft. If the bell is lowered 
into the water when atmospheric pressure is 14.7 lbs. per sq. in. and tempera- 
ture is 60° F., how far below the surface can the bottom of the bell be lowered 
if the water has a temperature of 40° F., weighs 62.5 lbs. per cu. ft., and is not 
to rise to a height of more than 4 ft. from the bottom of the bell? Assume that 
men and tools remain entirely within the air space, that they do not change 
volume with pressure change; that the air within the bell acquires the same 
temperature as the surrounding water. 

20. A quantity of heat equal to 1000 B.t.u. (= AQ) is given to an ideal 
gas maintained at constant volume. What are the numerical values of the 
several terms in the equation AQ = AS + A/ -f AE? 

21. Two pounds of a gas with Cy = 0.1662 and Cp = 0.2317 are heated at 
constant volume from a temperature of 60° F. to a temperature of 80° F., and 
then at constant pressure to a final temperature of 100° F. 

(a) How much heat is supplied by the gas? 

(b) What is the value of AS for each part of the process? 

(c) What is the value of AE for each part of the process? 

22. The true specific heat of a certain gas is 0.1733 in thermal units. The 
value of R is 55.16, what is the value of Cp for this gas? 

23. Three pounds of an ideal gas are heated until 200 B.t.u. per lb. have 
been supplied it. During the process the gas expands and 133,038 ft. -lbs of 
work are done by it. Find the value of AS. 

24. A balloon is filled with hydrogen gas at a pressure of 14.7 lbs. per sq. in 
and a temperature of 60° F. The balloon is spherical in shape and has an ' 
internal diameter of 25 ft. At a later time it is found that the pressure of the 
gas within the balloon is only 0.95 of the original value but that the tempera- 
ture is the same as before. What fraction of the original weight of gas must 
have escaped if the dimensions of the balloon have not changed? How much 
heat would have had to be removed to cause the pressure to fall to the same 
extent if no leakage occurred? (i lb. of hydrogen at 32° F. and 14.7 Ibs./sq. in. 
occupied a volume of 178 cu. ft. R = 766.5; Cp = 3.41.) What would be 
the final temperature? 

25. Ten pounds of air (specific volume at 32° and 14.7 lbs. = 12.387 cu. ft.) 
are contained in a receiver at a temperature of 55° F. and a pressure of 100 
lbs. per sq. in. Air leaks out until at a later time the pressure in the receiver 
is found to be only 40 lbs. per sq. in. with a temperature of 50° F. What 
weight has leaked out? 

26. An air receiver has a factor of safety of 5 when filled with air at a pres- 
sure of 200 lbs. per sq. in. and a temperature of 100° F. What amount of 
heat would have to be supplied the air to reduce the factor of safety to 2.5 on 
the assumption that the cubical content of the receiver remains constant with 
changing temperatures. {Cp = 0.2374; T — 1-4037.) 

27. The value of R for a certain gas is 34.9. How much external work 
will be done by five pounds of this gas if its temperature is raised from 50° F. 
to 150° F. at constant pressure? 

28. The value of Cp for a certain gas is 0.23 and the value of 7 is 1.39. 
What volume must this gas occupy when at a temperature of 60° F. and sub- 
jected to a pressure of 150 lbs. per sq. in.? 

29. A certain gas with molecular weight equal to 28 occupies a volume of 



PROBLEMS 753 

12.8 cu. ft. per lb. What volume will another gas with molecular weight of 
32 theoretically occupy when at the same temperature and pressure? 

30. A certain gas with molecular weight of 44 weighs 0.1224 lbs. per cu. ft. 
at standard conditions. Another gas has a molecular weight of 26. What 
is its theoretical density under the same conditions of temperature and 



pressure 



31. A water pump runmng at 50 strokes per minute delivers i cu. ft. of 
water per stroke. An air chamber is to be fitted to this pump of such size 
that the discharge pressure on the pump shall vary from 100 lbs. per sq. in. 
at the beginning of the stroke to 150 lbs. per sq. in. at the end of the stroke 
if all the water delivered during one stroke must be accommodated in the air 
chamber. The temperature of the water and of the air in the chamber re- 
main constant at 60° F. and no air is absorbed by the water, (a) What must 
be the volume of the air chamber if R for air is equal to 53.3? {b) Would 
there be any economic advantage in using a gas with i? = 96? 

32. Assume that gas is to be used for the doing of external work by being 
heated at constant pressure through a certain temperature range. If a large 
number of gases are available but only one pound of any one gas can be used, 
would you select the gas having the lowest or highest value of R if maximum 
amount of work was a consideration? Why? What other property of the 
gases would you consider if size of machine was also of importance? Why? 
Assuming that it is desired to determine the gas which would give the maxi- 
mum amount of work with the smallest machine, how would you proceed? 

CHAPTER V. 

1. (a) How much work can be done by two pounds of air expanding at a 
constant pressure of 50 lbs. per sq. in. to twice the original volume if the initial 
temperature is 50° F.? {b) What will be the final temperature? (c) How 
much heat will have to be supplied the gas? {Cp = 0.2374.) 

2. One-half pound of nitrogen is inclosed in a cylinder fitted with a fric- 
tionless piston. When the gas has a temperature of 100° F. the pressure upon 
the piston is 25 lbs. persq. in. It is desired to abstract 20 B.t.u. from the gas 
without changing its pressure. What will be the temperature drop and how 
much must the volume be decreased? (Cp = 0.2438.) 

3. A vessel with a capacity of 5 cu. ft. is filled with air at a pressure of 125 
lbs. per sq. in. when at a temperature of 60° F. It is desirable to lower the 
pressure to 50 lbs per sq. in. What amount of heat will have to be abstracted 
and what will be the final temperature of the gas, assuming that the vessel 
does not change in size with change of temperature? {R = 53.34; 7 = 1.4037.) 

4. A cylinder permanentlj' closed at one end is fitted with a frictionless 
piston and stands vertical upon its closed end in a vacuum. It holds a volume 
of I cu. ft. of gas at a temperature of 75° F., and a pressure of 20 lbs. per sq. in., 
the pressure being maintained by the weight of the piston and superposed 
discs of metal. The temperature is raised to 150° F. and the piston is pre- 
vented from rising by additional weights placed upon it. (a) What per- 
centage of the original weight of piston and discs must be added? (b) If no 
additional weights had been added how much external work would have been 
done by the expanding gas? 

5. How much work must be done to compress 100 lbs. of air isothermally 
from a pressure of 13 lbs. per sq. in. at a temperature of 70° F. to a pressure 
of no lbs. per sq. in.? (Spec. vol. at 32° F. and 14.7 lbs. = 12.387.) 

6. How much heat must be absorbed during the process assumed in prob- 
lem 4 above? 

7. One pound of air expands isothermally in a cylinder behind a frictionless 
piston. The initial pressure is 100 lbs. per sq. in., the initial temperature is 
50° F., the ratio of expansion is 5. (Spec. vol. at 32° F. and 14.7 lbs. = 12.387.) 
(a) What amount of work will the gas do upon the piston? (b) How much 
heat will have to be supplied the gas during the expansion? 



754 HEAT-POWER ENGINEERING 

8. Find the work done by 0.5 lb. of carbon dioxide expanding isothermally 
at 100° F. from an initial pressure of 100 lbs. per sq. in. to a final volume of 10 
cu. ft. (Spec. vol. at 32° and 14.7 lbs. = 8.1 cu. ft.) 

9. Air is compressed at constant temperature from a volume of 60 cu. ft. 
and a pressure of 14.7 lbs. per sq. in. to a volume of 12 cu. ft. Find (a) final 
pressure, (b) heat removed, and (c) work done upon the gas. 

10. Find the work done by 4 lbs. of air expanding isothermally from a 
pressure of 100 lbs. per sq. in. to 20 lbs. per sq. in., the final volume being 
80 cu. ft. 

11. Five pounds of air expand isothermally from a pressure of 120 lbs. per 
sq'. in. to a final pressure of 20 lbs. per sq. in., the work done being 248,500 ft.- 
Ibs. {R = 53.3.) Find (a) initial volume, (b) final volume, (c) initial tem- 
perature, and (d) heat supplied. 

12. The volume of i lb. of air at 32° F. and 14.7 lbs. per sq. in. = 12.387 
cu. in. (a) Find work done during the isothermal expansion of one pound of 
air from 100 lbs. per sq. in. to 20 lbs. per sq. in. at 100° F. (loge 5 = 1.61.) 
(b) Find initial and final volumes, (c) Find value of R. 

13. A given weight of gas occupies 3.09 cu. ft. and is under a pressure of 
200 lbs. per sq. in. It expands isothermally, the, ratio of expansion being 3. 
Find (a) final volume, (b) ft. -lbs. of work done, and (c) B.t.u. necessary to do 
this work. 

14. Atmospheric pressure at sea level on a certain day is 14.7 lbs. per sq. in. 
and on a certain mountain it is 12.5 lbs. per sq. in. An air compressor at 
each place compresses isothermally 100 cu. ft. of air per minute (measured at 
existing atmospheric pressure and same temperature in each case) to a pres- 
sure of 80 lbs. per sq. in. How much work is done upon the gas in each case? 
What is the difference, and what per cent of the smaller^quantity is used in 
excess in the less favorable location? 

15. If, in the preceding problem, each compressor had raised the pressure 
to five times atmospheric pressure at its own location, how would the quantities 
of work compare? 

16. A gas with 7 = 1.4 expands adiabatically from an initial volume of 10 
cu. ft. and an initial pressure of 100 lbs. per sq. in. to a terminal pressure of 
15 lbs. per sq. in. What is the final volume? 

17. A gas with y = 1.35 expands adiabatically from an initial volume of 
0.4 cu. ft. and an initial pressure of 80 lbs. per sq. in. to a final volume of 4 
cu. ft. What is the final pressure? 

18. A gas with 7 = 1.41 is compressed adiabatically from an initial volume 
of 5 cu. ft. and an initial pressure of 15 lbs. per sq. in. to a final volume of 
I cu. ft. What is the final pressure? 

19. A gas with 7 = 1.33 is compressed adiabatically from an initial volume 
of 2 cu. ft. and an initial pressure of 15 lbs. per sq. in. to a final pressure of 
85 lbs. per sq. in. What is the final volume? 

20. One pound of air expands adiabatically in a cylinder fitted with a 
frictionless piston. The initial pressure is 100 lbs. per sq. in.; the initial 
temperature is 50° F.; the ratio of expansion is 5. (Spec. vol. at 32° and 14.7 
lbs. = 12.387; 7 = 1.4037.) (ffl) What amount of work will the gas do upon 
the piston? (b) How much heat will have to be supplied the gas during the 
expansion? (c) Compare with results of problem 7. 

21. Five pounds of gas with 7 = 1.4 expand adiabatically from a volume 
of 0.2 cu. ft. and a pressure of 90 lbs. per sq. in. to a final pressure of 18 lbs. 
per sq. in. (a) What is the final volume? (b) How much external work is 
done by the gas? 

22. How much work must be done upon two pounds of gas to compress 
them adiabatically from a volume of 2 cu. ft. and a pressure of 14 lbs. per sq. 
in. to a final pressure of 80 lbs. per sq. in.? The value of 7 is 1.4. 

23. What will be the difference in the amounts of work required to com- 
press 5 cu. ft. of free air (air at 60° F. and 14.7 lbs. per sq. in.) to a pressure of 
90 lbs. per sq. in. when the compression is adiabatic and when it is isothermal? 
(7 = 1.4037.) 



PROBLEMS 755' 

24. Assume that an air compressor can be so arranged as to compress air 
either isothermally or adiabatically. It receives air at a pressure of 14 lbs. 
per sq. in. and compresses to a pressure of 75 lbs. per sq. in. (7 = 1.41.) (a) 
How much work would be done in compressing an initial volume of i cu. ft. 
of air by each method? {b) What would be the percentage of saving when 
using the more economical method? 

25. Five pounds of gas have an initial pressure of 300 lbs. per sq. in. and 
occupy an initial volume of 20 cu. ft. (Cp = 0.238; R = 53.3.) (a) Find 
Cv and Ti. (b) If this gas is expanded adiabatically to a pressure of 150 lbs. 
per sq. in., what will be the numerical value of V2, T2 and work done? 

26. One-quarter of a pound of gas with Cp = 0.238 and Cy = 0.169 is ex- 
panded adiabatically from Vi = 0.2 cu. ft. and pi = 300 lbs. per sq. in. to 
p2 = 150 lbs. per sq. in. (a) What are the numerical values of R, T, V2, T2? 
(b) What is the numerical value of work done? 

27. One-quarter of a pound of air is compressed adiabatically from 13 lbs. 
per sq. in. and 60° F. to a pressure of 100 lbs. per sq. in. After compression its 
temperature is decreased to 60° F. while the volume is maintained constant, 
(a) How much heat will have to be abstracted to bring this about? (b) What 
will be the final pressure? (c) If the gas is now allowed to expand adiabati- 
cally to a pressure of 13 lbs., how much work can it do and how does this 
compare with that required in the original compression? (d) What will be 
the volume and temperature at end of expansion as in (c) above? (Spec. vol. 
at 32° and 14.7 lbs. = 12.387; 7 = 1.4037; Cp = 0.2438.) 

28. Using logarithmic cross-section paper determine the pressure exerted by 
a gas for each cubic foot of volume increase when expanding according to the 
law P V^-35 = constant, from an initial pressure of 100 lbs. per sq. in. and an ini- 
tial volume of one and one-half cu. ft. to a terminal pressure of 15 lbs. per sq. in. 

29. Air is drawn into an air compressor at a temperature of 61° F. and at 
atmospheric pressure (14.7 lbs. per sq. in.). The flash point of the oil used 
to lubricate the compressor piston is 350° F. If compression is adiabatic, 
what pressure could be attained in the compressor if the maximum allowable 
temperature is 50 degrees below the fiash point of the oil? (Assume 7 = 1.41.) 

30. An air compressor compresses adiabatically 100 cu. ft. of air per min- 
ute measured at initial conditions of 15 lbs. per sq. in. and 60° F. The final 
pressure is 90 lbs. per sq. in. (a) Find work done on air per minute, (b) Find 
final temperature, (c) Find weight of air compressed per minute. (Spec, 
vol. = 12.387 at 32° F. and 14.7 lbs.; R = 53.3; and 7 = 1.41.) 

31. The initial conditions of two pounds of gas are pi = 100 lbs. per sq. in. 
and fi = 60° F. (R for this gas is 53.3 and 7 = 1. 41.) (a) How much work 
will be done by the gas if it expands isothermally to a final pressure of 15 lbs. 
per sq. in.? (b) If the expansion is adiabatic? (c) What is the percentage 
gain by the former method? (d) How is this gain purchased? (e) How do 
the final temperatures compare? 

32. Power is obtained by expanding air adiabatically in an engine cylinder. 
It is found that when the temperature of the air drops below 32° F. the mois- 
ture which is carried by the air freezes and. impairs the action of the engine. 
Air is received by the engine at a temperature of 60° F. and a pressure of 100 
lbs. per sq. in. (Assume 7 = 1.41 and assume further that the quantity of 
moisture present in the air is so small as to have no thermodynamic effect, 
i.e., all formulas may be used as though dry air only were present) (a) What 
is the lowest pressure to which the air can expand if its temperature is not to 
drop below 32° F.? (b) To what initial temperature would it be necessary to 
heat the air in order that it may be possible to expand to 15 lbs. per sq. in. 
without dropping below the minimum allowable temperature? 

33. Air is available for use in a compressed air engine at a temperature of 
65° F. and at a pressure of 125 lbs. per sq. in. It is desired to preheat it at 
constant pressure to such a temperature that it will not drop below a tempera- 
ture of 35° F. when expanded to a final pressure of 16 lbs. per sq. in. according 
to the equation PV^-^^= const. How much heat will be required per pound 
if Cp = 0.237? 



756 HEAT-POWER ENGINEERING 

34. How much work will be required to compress two pounds of gas from 
Vi = 25 cu. ft. and pi = 13.5 lbs. per sq. in. to p2 = 75 lbs. per sq. in. accord- 
ing to the equation PV^-^ = const.? What will be the final temperature if 
the initial temperature is 55° F.? 

CHAPTER VI. 

1. Is the following process thermodynamically reversible? Why? Gas in 
contact with a hot body with the same temperature as the gas, receives heat 
from that hot body while expanding isothermally and doing work. 

2. Is the following process thermodynamically reversible? Why? Gas 
expands isothermally and does a certain amount of work at the expense of 
heat received from a hot body at temperature 10 degrees higher than that of 
the gas. 

3. Is the following process thermodynamically reversible? Why? A gas is 
made to expand at constant pressure by being brought into contact with a 
hot body. 

4. Is the following process thermodynamically reversible? Why? A gas 
maintained at constant volume has its pressure decreased by being brought 
into contact with a cold body. 

5. Is the following process thermodynamically reversible? Why? Gas is 
compressed adiabatically in a nonconducting cylinder. 

6. Is the following process thermodynamically reversible? Why? Gas is 
compressed in a cylinder with metallic walls. 

7. Is the following process thermodynamically reversible? Why? A 
blacksmith strikes his anvil forcibly with his hammer. 

8. Is the following process thermodynamically reversible? Why? The 
hot gases resulting from the combustion of fuel within a boiler furnace flow 
up a smoke stack because their density is less than that of the atmosphere 
surrounding the stack. Is the process going on in the stack reversible? 

9. Is the following process thermodynamically reversible? Why? A car- 
penter bores a hole in a piece of wood by means of a brace and bit. 

10. Is the following process thermodynamically reversible? Why? A 
machinist cuts a thread upon a bar of metal which is rotated in a lathe. The 
bar and cutting tool are kept cool by a stream of soap solution. Outline the 
energy changes occurring and tell whether the process is reversible so far as 
these energy changes are concerned. 

11. Assume two vessels of equal cubical content arranged as in Sect. 35 (b), 
one containing one pound of air at a temperature of 60° F. and a pressure of 
100 lbs. per sq. in., the other absolutely void. (Spec, volume of air at 32° F. 
and 14.7 lbs. = 12.387). Assume that it is possible to open the cock between 
the two suddenly, to allow gas to flow from the high-pressure to the low-pres- 
sure vessel until both contain the same weight of gas. and then to close the 
cock suddenly so as to isolate the two bodies of gas. Assume further that 
the material of which the two vessels and fittings are made is absolutely 
impervious to heat, (a) At the end of the process what will be the tempera- 
ture of the gas contained in the vessel originally charged with high-pressure 
gas? {b) At the end of the process what will be the temperature of the gas 
contained in the vessel originally void? 

CHAPTER VII. 

1 . Find the change of entropy of 4 lbs. of a gas heated at constant pressure 
from a temperature of 60° F. to a temperature of 1000° F. {Cv = 0.192; 
R = 45-3-) 

2. If 6 lbs. of air are cooled at constant volume until the final pressure is 
one-fourth of the initial, find the change of entropy. {Cv = 0.169.) 

3. If ID lbs. of air are heated at constant pressure until k = 2 h, thereby 
adding 1185 B.t.u. to the gas, find the change of entropy. {Cp = 0.237,) 



PROBLEMS 757 

4. Find the entropy change of gas which is compressed isothermally from 
a pressure of 14.7 lbs. per sq. in. and a volume of 60 cu. ft. to a volume of 12 
cu. ft. The gas is maintained at a temperature of 80° F. 

5. If 25 lbs. of carbon dioxide, having R = 35.1, are compressed from a 
volume of 50 cu. ft. to a volume of 10 cu. ft., the pressure remaining constant, 
find the change in entropy. {Cp — 0.2008.) 

6. If 5 lbs. of air expand isothermally from a pressure of 100 lbs. per sq. in. 
to a pressure of 20 lbs. per sq. in. and a temperature of 60° F., find the change 
in entropy. {R = 53.3.) 

7. If h lb. of air is allowed to expand isothermally at a temperature of 70° F. 
until its final volume is 4 times its initial one, find its change in entropy. 
{R = 53-3.) 

8. Find the entropy change of 5 lbs. of a gas which expands isothermally 
at 60° F. until the ratio of its final volume to initial volume is 14.8. {Cp = 
0.2008; Cv = 0.1548.) 

9. Find how much heat would be required to heat 4 lbs. of air at constant 
volume so that it would experience an entropy change of 0.468, its initial 
temperature being 60° F. {Cv = 0.169.) 

10. 3 lbs. of air are compressed isothermally from a volume of 36 cu. ft. 
and pressure of 15 lbs. per sq. in. to a volume of 9 cu. ft. Find the change 
in entropy. {R = 53.3.) 

11. At the end of the compression stroke in a gas engine cylinder, the tem- 
perature is found to be 970° abs. and the entropy change from 32° F. is 0.55. 
After combustion at constant volume (pressure rise at const, vol.) the entropy 
has increased to 0.96. {Cv = 0.16.) 

(i) What is the final temperature at the end of combustion? 
(2) How much heat has been added? 

12. Imagine 0.4 lb. of an ideal gas to expand in a cylinder which prevents 
any heat flow to or from the gas, initial pressure being 100 lbs. per sq. in. and 
initial volume § cu. ft., find the work done when its volume has become 3 cu. ft. 
Find change in temperature. Find the change in entropy. {Cp = 0.124. 
Cv = 0.093.) 

CHAPTER Vni. 

1. A Carnot cycle is performed with gas as a working substance. The 
temperature of the hot body is 1000° F. and that of the cold body is 60° F. 
How much work is done per cycle if the heat supplied per cycle is 10 B.t.u.? 

2. In the case of the Carnot cycle as above with higher temperature 
1000° F. and lower temperature 60° F., how much work would be done per 
cycle if the heat rejected per cycle equals 10 B.t.u.? 

3. A Carnot cycle with gas as working substance is used for the develop- 
ment of power. It is desired to obtain 100 ft. -lbs. of work per cycle. The 
heat supplied per cycle equals 0.3 B.t.u. and the temperature of the hot body 
is 500° F. What must be the temperature of the cold body? 

4. A Carnot engine is to be used as a heat pump to remove 10 B.t.u. per 
cycle from a body at a temperature of 32° F. and discharge to a body at a 
temperature of 100° F. (a) How much energy will be required per cycle to 
operate this heat pump? {b) How much will be required if the upper tem- 
perature is 200° F.? (c) How much heat will be discharged to the hot body 
in each case? 

5. An engine using air as a working substance, receiving heat from a hot 
body at temperature 1000° F. and rejecting at temperature 100° F., operates 
on a cycle composed of an isothermal expansion, an adiabatic expansion, an 
isothermal compression, and an isovolumic. Is this a reversible cycle? Why? 

6. Draw cycle described in 5 above and determine: 

(i) Heat supply (positive or negative) during each process. 

(2) Work done (positive or negative) during each process. 

(3) Efficiency of cycle. 

(4) Carnot efficiency with same temperature limits; 7 = 1.41; R = 53.3; 
W = I lb.; /• = 2 for the isothermal expansion. 



758 HEAT-POWER ENGINEERING 

7. One-quarter of a pound of air is enclosed in a cylinder fitted with a 
moveable piston. It occupies a volume of 3 cu. ft., exerts a pressure of 100 
lbs. per sq. in., and the area of the piston is i sq. ft. The gas is expanded at 
constant pressure to a volume of 6 cu. ft.; the pressure is then dropped at 
constant volume to a value of 15 lbs. per sq. in.; the gas is then compressed 
at constant pressure to a volume of 3 cu. ft.; lastly the pressure is raised to 
100 lbs. per sq. in. at constant volume. 

(a) Draw the cycle to PV coordinates and indicate values of pressure, vol- 
ume and temperature at the four corners. 

(b) Find the net work done by the gas during one cycle. 

(c) Find the heat supplied or rejected during each process and the net heat 
change. 

(d) Find the efficiency of the cycle. 

(e) Assuming the use of one hot and one cold body is this cycle reversible? 
Why? 

8. (a) Draw the Carnot cycle to PV and T<^ coordinates for the following con- 
ditions. Two pounds of nitrogen are used as working substance. The maxi- 
mum temperature is 1500° F. and the maximum pressure is 200 lbs. per sq. in. 
The ratio of isothermal expansion is 2. The minimum temperature is 50° F. 

(b) Find the heat supplied, the heat rejected and the work done. 

(c) Find the efficiency of the cycle, or of an engine using the cycle. 

9. (a) Determine the efficiencies of Carnot cycle engines using gaseous 
working substances when the hot body and the cold body have the following 
temperatures respectively: 



Body Temperature 


Cold Body Temperature 


(1) 3000° F. 

(2) 1500° F. 

(3) 1500° F. 


500° F. 

o°F. 

500° F. 



(b) Which is the more effective method of increasing the efficiency, raising 
Ti or lowering T'^? Why? 

10. If the maximum and minimum temperatures and pressures are both 
given, what must be the ratio of isothermal expansion in a Carnot cycle engine 
using gas as a working substance? 

11. An engine operating on the Joule cycle has the following conditions at 
the end of compression Va = 0.5 cu. ft.; pa = 70 lbs. per sq. in.; Ta = 1800° 
abs. After constant pressure expansion the volume is 0.75 cu. ft. For the 
gas used Cp = 0.26 and Cv = 0.13. Temperature at end of expansion is 900° 
abs. and at the beginning of compression is 600° abs. Find 

(i) Net work of cycle. 
(2) Efficiency of cycle. 

12. A gas engine operating on the Otto cycle uses 0.15 lb. of gas per cycle 
having Cp = 0.1028, C„ = 0.0514 and R = 40. The pressure at end of com- 
pression is 75 lbs. per sq. in. and the temperature is 1000° abs. At end of 
explosion line the temperature has risen to 2500° abs. ; at the end of expansion 
the temperature is 1800° abs. and at the beginning of compression it is 720° 
abs. Find: 

(i) Work during expansion and compression. 

(2) The heat sent into, and the heat sent out of, the system. 

(3) The efficiency of the cycle. 

13. A gas engine operating on the Diesel cycle uses an oil, the products of 
combustion of which have a gamma value of 1.41. The weight of gas used is 
0.15 lbs. The temperature at end of compression is 1800° abs. and at end 
of constant pressure expansion is 2000° abs. The clearance is 8 per cent and 
the piston displacement is 2 cu. ft. (Cp = 0.2056, Cv = 0.1457.) Find: 

(a) Heat added. 

(b) Heat rejected. 

(c) The pressure obtained at beginning and end of each process. 

(d) The entropy changes for each line. 



PROBLEMS 759 

14. A Rider hot air engine, operating on the Stirling cycle, uses 0.066 lbs. 
of air. The temperature of the hot body is 2000° abs. and that of the cold 
body is 600° abs., the initial volume being 0.8 cu. ft. and the final volume 
being i cu. ft. {Cp = 0.237, Cv = 0.169.) Lowest pressure in cycle = 14.7 
lbs. per sq. in. Find: 

(a) The pressures at the beginning and end of expansion, and at the end of 
compression. 

{b) Net work of cycle. 

15. A Diesel gas engine operates with a gas having Cp = 0.22 and Cv = 
0.156 with an i? = 70. The pressure at the end of compression is 550 lbs. per 
sq. in.; the volume is o. i cu. ft. and the temperature 2000° abs. At the 
beginning of the adiabatic expansion the temperature is 2400° abs. and at 
the end of same it is 1200° abs. Find all necessary temperatures, pressures 
and volumes to determine: 

(a) The work done during the constant pressure and adiabatic expansions. 
{b) Work during adiabatic compression, 
(c) Efficiency of cycle. 

16. A gas engine working on the Otto cycle has a pressure at the beginning 
of compression = 13 lbs. per sq. in. Find the clearance to give a com- 
pression of 91 lbs. per sq. in., assuming the exponent for compression to be 
1.22. If the initial temperature is 60° F. find the temperature at the end of 
compression. 

17. Suppose a gas engine is working on the Otto cycle, under the following 
conditions: Compression pressure = 80 lbs. per sq. in.; pressure after ex- 
plosion = 240 lbs. per sq. in. The volume at the beginning of compression is 
6 cu. ft., and at the end of compression it is 2 cu. ft. (7 = 1.41.) Find work 
done for each step of cycle and the net work done. 

18. With the same data as in the previous problem, find the efficiency of 
the cycle, the heat supplied per cycle and the heat rejected. 

19. If a gas engine working on the Otto cycle has 25 per cent clearance, find 
the efficiency of the cycle. (7 = 1.41.) 

20. Find the horse power of a gas engine making 100 cycles per minute, 
each cycle transforming 50 B.t.u. into work. 

21. How many B.t.u. per minute will be required to develop 100 H.P. in a 
single-acting 4-stroke cycle gas engine running 200 R.P.M. if the efficiency of 
the cycle is 30 per cent? What would be the heat input per cycle? 

CHAPTER IX. 

1. If liquid with a constant specific heat equal to 0.5 vaporizes at a tem- 
perature of 150° F. when the pressure is atmospheric and solidifies at 2°F.; 
(a) What is the value of q for atmospheric pressure figured above the tempera- 
ture of fusion? {b) What is the value of g figured above 32° F. as a datum? 

2. A certain liquid has a variable specific heat given by the following equa- 
tion, Cp = 0.7 -|- 0.003 / — o.oooi /- in which t stands for temperature in 
Fahrenheit degrees. It vaporizes at a temperature of 100° F. under atmos- 
pheric pressure and solidifies at — 35° F. What is the numerical value of 
the heat of the liquid figured above temperature of fusion as a datum? 

3. When one pound of a certain liquid vaporizes under a pressure of 
35 lbs. per sq. in., there is a volume change of 50 cu. ft. The total amount of 
heat added to cause vaporization of liquid already at vaporizing temperature 
is 900 B.t.u. {a) What is the numerical value of the latent heat of vapor- 
ization? {b) What is the numerical value of the external latent heat of 
vaporization? . (c) What is the numerical value of the internal latent heat of 
vaporization? 

4. A certain liquid has a constant specific heat of 0.85; it solidifies at 
— 25° F. and vaporizes under a pressure of 50 lbs. per sq. in. at a temperature of 
175° F. The total heat required to raise the temperature of one pound of 
material from 60° F. and so cause total vaporization at a pressure of 50 lbs. per 
sq. in. is equal to 1250 B.t.u. (a) What is the numerical value of q for these 



76o 



HEAT-POWER ENGINEERING 



conditions, figured above fusion temperature as a datum? (b) What is the 
numerical value of r for these conditions? (c) What is the numerical value 
of X for these conditions? 

5. The pressure of a certain saturated vapor at a temperature of 250°. F. 
is 75 lbs. per sq. in. What will be the temperature of vaporization of this 
material under a pressure of 75 lbs. per sq. in.? 

6. The latent heat of vaporization of a certain material under certain con- 
ditions is 525 B.t.u. and the heat of the liquid is 210 B.t.u. What will be the 
heat above the chosen datum associated with 5 pounds of the vapor of this 
material when it has a quality of 85 per cent? 

7. Three-quarters of a pound of liquid and one-quarter of a pound of the 
vapor of that liquid have been standing in a closed vessel for a considerable 
length of time. The temperature of the liquid is 75° F. (a) What is the con- 
dition of the vapor? Why? (Z>) What is the temperature of the vapor? Why? 

8. The average constant pressure specific heat of a certain vapor over a 
temperature range of 100 degrees starting at the temperature of vaporization at 
a pressure of 100 lbs. per sq. in. is 0.4. The internal latent heat of vaporization 
at this pressure is 700 B.t.u. The external work done during vaporization is 
46,600 ft. -lbs. The specific heat of the liquid is constant and equal to 0.9 
over the temperature range of 200 degrees between datum temperature and 
the temperature of vaporization under the pressure given above. What is 
the total heat associated with 10 lbs. of this superheated vapor at a temper- 
ature of 100 degrees higher than its temperature of vaporization at the assumed 
pressure? 

9. A certain material has a latent heat of vaporization of 700 B.t.u. at 
atmospheric pressure. The constant pressure specific heat of its super- 
heated vapor at atmospheric pressure is 0.5. If 7 lbs. of this superheated 
vapor are brought into intimate contact with 5 lbs. of 75 per cent vapor of the 
same material and the combination is maintained at atmospheric pressure, 
what will be the ultimate condition of the resulting product? 

10. A gas occupying a vessel with internal volume of i cu. ft. exerts a 
pressure of 10 lbs. per sq. in. Another gas in a similar vessel exerts a pressure 
of 15 lbs. per sq. in. What will be the pressure on the walls if both gases 
simultaneously occupy one of the vessels? 

11. A certain space is saturated with a vapor at a temperature of 250° F. 
which exerts a pressure of 17 lbs. per sq. in. Air at the same temperature as 
the vapor is pumped into the same space until the pressure has risen to 25 lbs. 
sq. in. What weight of air occupies each cubic foot of the space if the spe- 
cific volume of air at 32° F. and 14.7 lbs. per sq. in. is 12.387? 

12. A certain liquid is vaporized in a closed vessel from which the vapor is 
allowed to escape as fast as generated. The pressure of the vapor in question 
at the temperature within the vessel should be 100 lbs. per sq. in. but a pres- 
sure gauge indicates a pressure of 102 lbs. per sq. in. The excess is supposed 
to be due to air mixed with the vapor. The value of R for air is 53.34. How 
much air must be present per cubic foot of space? 

CHAPTER X. 

1. By means of the steam table find the temperature, total heat, heat of 
the liquid, internal latent heat, and external latent heat for one pound of dry 
saturated steam having the following absolute pressures in lbs. per sq. in.: 
15, 50, 80, 125, 175 and 300. 

2. Determine from the steam table the space filled by 10 lbs. of dry satu- 
rated steam under an absolute pressure of 200, 175, 135, 100, 80 and 10 lbs. 
per sq. in. 

3. By means of the steam table determine the number of pounds of steam 
that will be required to fill 10 cu. ft. when under an absolute pressure of 200, 
115, 40 and 5 lbs. per sq. in.: (a) If the quality is 100 per cent; (b) If the 
quality is 80 per cent. 

4. Determine by means of the steam table the entropy of the liquid, and 



PROBLEMS 761 

the entropy of vaporization for i lb. of steam under the following absolute 
pressures: 15, 50, 80, 125, 175, and 300 lbs. per sq. in. (a) If the quality is 
100 per cent. (6) If the quality is 90 per cent. 

5. Assuming the specific heat of water to be unity, compute the entropy of 
the liquid for a pound of water heated to the point of vaporization for an abso- 
lute pressure of 100 lbs. per sq. in. Find the per cent error by comparison 
with steam table values. 

6. Compute the entropy of vaporization for a pound of steam having the 
following temperatures: 400, 300 and 200° F., the corresponding latent heats 
being 827.2, 909.5 and 977.8 B.t.u. 

7. (a) Determine from the steam tables the amount of heat required to 
make a pound of steam, having a pressure of 100 lbs. per sq. in. abs., by heat- 
ing the water to the temperature of vaporization from a temperature of 100° F., 
and then vaporizing until the quality is 80, 90 and IQO per cent. 

(6) Draw the T^-diagram for (a). 

8. With the same data as in (7) find: 

(a) The amount of heat required to superheat the steam 100°, 200°. Take 
Cp — 0.50. {b) Draw the T(^-chart for (a). 

9. Determine by means of the steam table the quality of steam containing 
1029 B.t.u. of intrinsic heat and having a pressure of 125 lbs. per sq. in. abs. 

ID. Determine by means of the steam table the intrinsic heat added to 
I lb. of water in heating it from 90° F. to 444° F., if the pressure is keot con- 
stant at 120 lbs. per sq. in. abs. 

11. Heat is added to i lb. of steam at a constant pressure of 80 lbs. per sq. 
in. abs., thereby increasing the quality from 0.4 to 0.9. Find by means of 
steam tables: (a) How much heat is added, {b) How much internal heat is 
added. (c) How much external heat is added. {d) How much work in ft.- 
Ibs. is done, (e) How much the volume of the steam is increased. 

12. Find by means of the steam table the heat required to evaporate 50 lbs. 
of water having a temperature of 102° F. when pumped into a boiler, the steam 
pressure in which is 125 lbs. per sq. in. abs. 

13. If the temperature of the feed water is 200'^, find by means of the 
steam table the amount of heat required to make 100 lbs. of steam having a 
quality of 95 per cent, the pressure being constant at 175 lbs. per sq. in. abs. 

14. By means of the steam table determine the volume occupied by the 
steam in the previous problem. 

15. Compute the external work performed in vaporizing 4 lbs. of water 
into dry steam under a constant pressure of lOO lbs. per sq. in. abs. Com- 
pare with tabular value. 

16. Find the pressure equivalent to the internal force which must be 
overcome in vaporizing i lb. of water under a pressure of 100 lbs. per sq. in. abs. 

17. Steam in a boiler is under an absolute pressure of 100 lbs. per sq. in., 
and is superheated 150.6°. 

(a) Find by Tumlirz equation the specific volume of this steam. 
(&) Find the total heat of this steam if its specific heat is 0.51. 
(c) Show part (6) on a T</>-chart. 

18. Find the heat of superheat, and the total intrinsic heat energy for the 
steam in the previous problem. 

19. Sketch on a T(^-chart the water curve and saturation curve for a pound 
of water vapor between the pressure limits of 2 and 200 lbs. per sq. in. abs. 
showing the intermediate values for the following pressures, 10, 50 and lOO. 

(a) Mark on the sketch the value of the temperature and the entropy for 
each point, estimating the distances as closely as possible. 

(&) Give the numerical values for, and show what areas represent, the heat 
of the liquid, and the latent heat for the two limiting pressures given above. 

(c) If you had drawn the above sketch to the following scale: i" = 100° of 
temperature and i" = I unit of entropy, how many sq. in. would represent the 
total heat of the steam for the pressure of 200 lbs. per sq. in. abs.? Indicate 
this area on your sketch. 

20. Find the volume of a boiler containing looo lbs. of water and 6 lbs. of 



762 HEAT-POWER ENGINEERING 

dry saturated steam under a pressure of 135 lbs. per sq. in. abs. What per 
cent of this volume is occupied by each.'' What per cent of the total heat 
energy above 32° is contained in each.-* 

21. How much water having a temperature of 60° F. will be required to 
condense 3000 lbs. of steam per hour, the quality of the steam being 90 per 
cent and the pressure within the condenser being i lb. per sq. in. abs..'' How 
much, if the condenser pressure is 5 lbs. per sq. in.? Assume the cold water to 
be thoroughly mixed with the steam. 

22. Four pounds of steam having an absolute pressure of 125 lbs. per sq. 
in. are condensed by flowing into 200 lbs. of water, the temperature of which 
is thereby raised from 60 to 80° F. Find the initial qualit}^ of the steam. 

23. Find the total heat necessary to change 500 lbs. of water from a feed 
pump temperature of 80° F. into superheated steam having a temperature 
of 1000° F., the boiler pressure remaining constant at 125 lbs. per sq. in. abs. 
Take the specific heat of superheated steam for this range to be 0.50. 

24. One pound of water at a temperature of 60° F. enters a boiler and is 
vaporized under a pressure of 115 lbs. per sq. in. abs. until it becomes dry and 
saturated steam. How many pounds of water might have been vaporized if 
the same amount of heat had been added to the water at a temperature of 
212° and changed into dry steam at this temperature? 

25. How much steam with a quality of 90 per cent and an absolute pressure 
of 3.45 lbs. per sq. in. is condensed in a surface condenser using 14,500 lbs. of 
circulating (or condensing) water per hour, the water entering the condenser 
at 55° F. and leaving it at 115° F.? 

26. An engine develops 15 horse power using 28 lbs. of steam per horse- 
power hour. If the engine exhausts its steam with a quality of 85 per cent and 
pressure of 15 lbs. per sq. in. abs. to the atmosphere, find the amount above 
32° F. discharged per minute. What would be the maximum amount of heat 
that could be abstracted per minute from this exhaust steam by means of 
water which is to attain a temperature of 200°? 

27. For each pound of coal having a heating value of 14,300 B.t.u., a certain 
boiler evaporated 10 lbs. of water into steam, with quality of 95 per cent, the 
pressure being constant at 145 lbs. per sq. in. abs., and the temperature of 
the feed water being 188° F. 

Suppose that another boiler, using this same kind of coal, evaporated 9 lbs. 
of water into dry steam, under constant pressure of 125 lbs. per sq. in., from 
a feed water temperature of 121° F. 

Find the heat given water and steam by each boiler, and the boiler efficiencies 
(efficiency = heat supplied water and steam h- heat supplied boiler). 

28. Determine by means of the T<;6-diagram the pressure at which steam 
will become dry and saturated by expanding reversibly and adiabatically 
from a pressure of 100 lbs. per sq. in. and a superheat of 50° F. 

29. Determine by means of the T0-diagram the final condition of steam 
which expands reversibly and adiabatically from an initial superheat of 150° F. 
at a pressure of 150 lbs. per sq. in. to a final pressure of 15 lbs. per sq. in. 

30. Determine by means of the T^-diagram the volume of 10 lbs. of 80 
per cent steam at a pressure of 75 lbs. per sq. in. 

31. By means of the values given in the steam table draw a T^-diagram 
for steam to such a scale as to show the extreme upper parts of the water and 
saturation fines. Explain the shape produced. 

32. Draw by means of values given in the steam tables a physical equil- 
ibrium diagram for liquid water and water vapor between the critical tempera- 
ture and 100° F. similar to part of Fig. 34. (Use care in choosing scales so 
that entire diagram can be drawn on sheet chosen.) 

33. Determine by means of the Mollier Chart the final conditions of steam 
expanding reversibly and adiabatically from an initial superheat of 400 degrees 
at a pressure of 100 lbs. per sq. in. to a final pressure of 10 lbs. per sq. in. 

34. Find from the Mollier Chart the heat which must be supplied to change 
10 lbs. of 95 per cent steam at 20 lbs. per sq. in. to steam superheated 200 
degrees F. at the same pressure. 



PROBLEMS 763 



CHAPTER XI. 



1. One pound of dry saturated steam at an absolute pressure of lOO lbs. per 
sq. in. is expanded along a reversible adiabatic until its pressure is 50 lbs. per 
sq. in. abs. Find its new quality, volume and the work done. 

2. Find the same quantities with the same data as in the previous problem, 
except the second pressure, which is 15 lbs. per sq. in. 

3. Steam is formed in a boiler at a constant pressure of lOO lb. per sq. in. abs. 
and with such a quality that a pound occupies only 3.54 cu. ft. Heat is added 
at constant pressure until the steam is superheated 150 degrees. (a) Deter- 
mine the quality at the beginning of the superheating process, {b) Find the 
total heat added and the heat of superheat, (c) Show on T</)-chart. 

4. How much external work was done in the previous problem during the 
period of superheating? What is the total intrinsic heat energy at the point 
of maximum superheat? 

5. Steam is contained in a cylinder, at an absolute pressure of 125 lbs. per 
sq. in. and a quality of 80 per cent. It expands isentropically to 25 lbs. per 
sq. in. abs. (a) Find volume occupied by steam before expansion {b) Find 
quality at end of expansion, (c) Find work done in ft. -lbs. during adiabatic 
expansion. 

6. For previous problem find the total heat of steam at the beginning and 
at the end of expansion; also the intrinsic heat energy used up in expanding 
adiabatically. 

7. Steam with a superheat of 200 degrees and an absolute pressure of 125 
lbs. per sq. in. expands at constant entropy in a cylinder, until its pressure 
has been reduced 80 per cent. How much work has been accomplished? 

(a) What is the total heat of the steam at point of maximum superheat? 
(&) Show on PV- and T</)-charts. 

8. If the steam of previous problem expands further to 15 lbs. per sq. in., 
find quality and intrinsic heat at end of the expansion. 

9. Steam in a cylinder at a pressure of 25 lbs. per sq. in. abs. and a quality 
of 90 per cent is compressed along a reversible adiabatic until just dry and 
saturated. 

(a) What are the temperature, pressure, and specific volume at end of com- 



pression 



10. Steam at an absolute pressure of 175 lbs. per sq. in. is confined in a 
metal cylinder. Heat is abstracted at constant volume until its temperature 
becomes 240° F. 

(a) Find the quality at the end of change. 

{b) Find the amount of heat abstracted during the process. 

(c) Show on PV- and T(^-fields. 

11. Superheated steam exists in a cylinder at a pressure of 25 lbs. per sq. 
in. abs. and a temperature of 366° F. 

(a) Determine volume of steam at this point. 

(b) Isothermal compression occurs until the steam is just dry and saturated; 
how much heat has been abstracted? Show on T^-chart. 

12. Steam at a pressure of 125 lbs. per sq. in. abs. and a quality of 80.4 
per cent has he^t abstracted at constant volume until the pressure becomes 
15 lbs. per sq. in. abs. 

(a) Find quality at end of the process. 

(6) Find volume at beginning and end of process. 

(c) Find intrinsic heat change during process. 

13. One pound of steam under a pressure of 120 lbs. per sq. in. abs. expands 
isentropically until its pressure is reduced 50 per cent; find its new quality, 
if its initial qualit}^ was 0.2, 0.4, 0.6, 0.8, i.o. Show each of the above expan- 
sions on T0-chart. Tabulate results. 

14. If a pound of dry saturated steam under a pressure of 150 lbs. per sq. in. 
abs. is cooled at constant volume to a temperature of 59° F., find its new 
-quality, pressure and the heat removed. Show on T0-chart. 

15. Steam with 70 per cent quality is heate"d at a constant pressure of 125 



764 HEAT-POWER ENGINEERING 

lbs. per sq. in. abs. until it becomes just dry and saturated. More heat is then 
added isothermally until a pressure of 25 lbs. per sq. in. abs. is reached. 

(a) Find heat added during both processes. 

(b) Find intrinsic heat gained during each operation. 

16. If a pound of steam with quality of 70 per cent and pressure of 20 lbs. per 
sq. in. abs. has heat removed from it while maintained at constant volume, 
thereby reducing its pressure to 15 lbs. per sq. in. abs., find its final quality 
and the heat removed. 

17. Dry saturated steam having a pressure of 165 lbs. per sq. in. abs. has heat 
abstracted from it while maintained at constant volume until its pressure 
becomes 25 lbs. per sq. in abs. 

(a) Find the heat abstracted. 

(b) Find the final quality of the steam. 

(c) Find intrinsic heat change during process. 

18. Fifteen pounds of dry saturated steam under a pressure of no Ibs./sq. 
in. abs. are enclosed in a metallic tank, and this tank is then immersed in 
1000 lbs. of water at a temperature of 60° F. If the tank is left in the cold water 
until the pressure within has reached atmospheric (14. 7), find the temperature 
of the cold water and the quality of the steam. (Assume the tank to be a 
perfect conductor and that there are no heat losses.) 

19. Given a pound of steam with a quality of 80 per cent and a pressure of 
100 lbs. persq. in. abs. Find the heat required and the work done to double 
its volume at constant pressure. 

20. Suppose a pound of dry saturated steam having an absolute pressure of 
150 lbs. per sq. in. expands isothermally until its volume is doubled; find the 
work done, heat supplied and final pressure. 

21. Work previous problem, starting with the steam having a quality of 
45 per cent. 

22. Find the work done in ft. -lbs. in superheating one pound of steam 
100 degrees at a constant pressure of 68 lbs. per sq. in. abs. Find the change 
in the intrinsic energy of the steam. Find the change in volume and the exter- 
nal work. 

23. Suppose one pound of steam under an abs. pressure of 100 lbs. I sq. in. 
and a quality of 90 per cent expands along reversible adiabatic to a pressure 
of 2 Ibs./sq. in. abs. Find its new quality, volume and the work done. 

24. Suppose the steam in the previous problem to have been superheated 
200 degrees; find the same quantities. 

25. Given a pound of steam under a pressure of 15 Ibs./sq. in. abs. and 
quality of 50 per cent. If heat is added while it is maintained at constant 
volume until its quality is unity, find the heat required, the final temperature 
and the pressure. 

CHAPTER XII. 

1. An engine using water vapor and operating on the Carnot cycle, as in 
Sect. 91, between the pressure limits of 185 lbs. and 25 lbs. per sq. in. begins 
adiabatic expansion at 80 per cent quality. 

(a) Find the qualities at end of expansion and at beginning of adiabatic 
compression. 

(b) Find the work accomplished in ft. -lbs. 

(c) Find the efficiency of the cycle by two methods. 

(d) Show the cycle on both PV- and T^-fields. 

2. With the same initial temperature and the same back pressure as in 
previous problem, suppose adiabatic expansion to start from a point in the 
superheated region where the pressure is 60 lbs. per sq. in. Cp = 0.53. 

(c) Determine conditions of the steam at the end of the adiabatic expansion. 

(b) Find the work accomplished in ft. -lbs. 

(c) Find the efficiency of the cycle. 

(d) Show the cycle on both PV- and T</)-fields. 

3. Given the initial pressure of a Carnot Cycle with steam as working sub- 
stance at 135 lbs. per sq. in. and the final pressure 25 lbs. per sq. in. The 



PROBLEMS 765 

isothermal expansion starts with water and the steam at the beginning of 
adiabatic expansion is just dry and saturated. 

(a) Find the heat added and the heat rejected. 

{b) Find the intrinsic energy at the beginning and end of each Hne of the 
cycle. 

(c) Find the efficiency of the cycle. 

[d) Show on T^-chart. 

4. What is the efficiency of the Carnot cycle for a steam engme receiving 
dry saturated steam at a pressure of 150 lbs. per sq. in. abs. and exhausting it 
at a pressure of 15 lbs. per sq. in. abs. 

Show on the PV- and T</)-charts. 

5. If the exhaust pressure in the previous problem had been 2 lbs. per sq. 
in. abs. what would have been the efficiency? 

Show on PV- and T^-charts. 

6. If the engine in problem 4 exhausts 8000 B.t.u. per min., what is its 
power? 

7. If the engine in problem 5 exhausts 8000 B.t.u. per min., what is its 
power? 

8. The adiabatic expansion of a Carnot cycle which starts with liquid 
at the temperature of vaporization begins with a steam pressure of 25 lbs. per 
sq. in. abs. and a temperature of 344.4° F. 

This expansion ends when a temperature of 213° F. has been reached. 
Find the heat supplied, heat rejected and the efficiency of the cycle. Check 
the efficiency by a second method. 

Show on T<^-chart. 

9. If the cycle of the previous problem were reversed, and we were to use 
some suitable working substance, what would be the coefficient of perform- 
ance for a cooling machine? For a warming machine? 

(Coef . of perf. = result -j- expenditure.) 

Show on the T0-chart. 

10. An engine working on the Carnot cycle transforms 113.94 B.t.u. 
into work per cycle. If the temperature of the steam initially is 358.5° F. 
and finally 250.3° F., find the initial state of the steam. Show on the 
T(^-chart. 

11. If a steam engine, working on the Carnot cycle with an efficiency of 
20 per cent requires 3000 lbs. of dry saturated steam per hour the pressure 
being 100 lbs. per sq. in. abs., find the exhaust pressure. How much heat does 
the condenser remove per hour? What is the horse power of this ideal engine? 
Show on the T</)-chart. 

12. If a boiler supplies dry saturated steam with a pressure of 150 lbs. per 
sq. in. abs. to an engine operating on the Carnot cycle, in which the back 
pressure is 5 lbs. per sq. in. abs., find the work done, the heat flow for each 
path, the net work of the cycle, and its efficiency. Show on Ti^- and PV- 
charts. Check your net work by another method. 

13. Solve previous problem starting with a quality of 90 per cent. 

14. An engine operates on the Clausius cycle between the pressure limits 
of 185 lbs. per sq. in. and 25 lbs. per sq. in. Adiabatic expansion occurs from 
a temperature of 575° F. Cp = 0.52. (a) Determine the total heat added 
AQi. {h) Determine the total heat rejected ^.Qi. (c) Determine the work 
accomplished during adiabatic expansion, {d) Find the efficiency of the cycle. 

15. Suppose the engine of the previous problem to operate on the Rankine 
cycle with release at 25 lbs. per sq. in. and a back pressure of 5 lbs. per sq. in. 
abs. (a) Determine the efficiency of this cycle. (Jb) What would be the 
efficiency of a Carnot cycle operating between the same temp, limits. 

16. Find the difference in the heat supplied, heat rejected, work done and 
the efficiency of a Carnot and Clausius cycle when each engine receives dry 
saturated steam having an abs. pressure of iio lbs. per sq. in., the back pres- 
sure being 20 lbs. per sq. in. abs. 

Show on the PV- and T^-charts. 



766 HEAT-POWER ENGINEERING 

17. Find the heat supphed, heat rejected, work done and the efficiency of 
an engine working on the Clausius cycle receiving steam with a pressure of 
140 lbs. per sq. in. abs. and 150° of superheat, if the exhaust pressure is 15 lbs. 
per sq. in. abs. 

Show the PV- and T^-charts. 

18. Find the heat supplied, heat rejected, work done and efficiency of an 
engine working on the Rankine cycle in which the initial steam pressure is 
130 lbs. per sq. in. abs. with 150° of superheat; and the temperature at the end 
of adiabatic expansion is 240.1° F. while the exhaust pressure is 15 lbs. per sq. 
in. abs. 

Show on PV- and T<^-charts. 

19. Given a feed pump cycle (rectangular PV-diagram) working between 
the pressure limits of 135 lbs. per sq. in. and 15 lbs. per sq. in. The steam 
is superheated 100° F. {Cp = 0.55.) (a) Find the volume of the cylinder re- 
quired, {h) Find the efficiency of the cycle, (c) Show on PV- and T0-charts. 

20. Find the heat supplied, heat rejected and work done per pound and 
the efficiency of a feed pump cycle in which the heat abstraction begins when 
the steam has a pressure of 140 lbs. per sq. in. abs., and 50° of superheat. The 
constant volume change ends when a temperature of 213° F. has been reached. 

21. Suppose an engine working on the Rankine cycle receives dry satu- 
rated steam having a pressure of 200 lbs. per sq. in. abs., then expands it until 
its pressure drops 90 per cent. The condenser pressure is 4 lbs. per sq. in. abs. 

(a) Find the efficiency of the cycle. 

{b) If the engine requires j of a pound of steam per cycle find the volume 
of the cylinder necessary for this ideal cycle. 

(c) With the same data as in {b) find the horse power if the engine runs 300 
cycles per min. 

id) Plot the PV- and T^-charts for this cycle estimating distances as closely 
as possible. 

{e) What is the horse power per cu. ft. of piston displacement? 

22. With the same initial steam and the same back pressure as in previous 
problem, find the same quantities for the Clausius cycle. 

23. With the same initial steam and the same back pressure as in 21 
find the same quantities for the cycle in which there is no expansion of the 
steam. 

CHAPTER XIII. 

1. How much heat is transformed into work by an engine delivering 100 
h.p. for 24 hrs.? 

2. Find the i.h.p. of a lo-in. by 12-in. engine, double acting, running 200 
rev. per min. when the m.e.p. from the indicator diagram is 30 lbs. per sq. in. 

3. Suppose the engine of the previous problem had given an indicator 
diagram, having an area of 2.y sq. in., and a length of 3 in. If the scale of 
the spring used in the indicator had been 50 lbs. per in., find the i.h.p. 

4. An engine 18 in. by 24 in., double acting, running 150 rev. per min. 
delivers 100 b.h.p. If the indicator diagram gives a m.e.p. of 25 lbs. per sq. 
in., find its mechanical efficiency, and the friction horse power. 

5. Suppose the same engine, running at the same speed as in the previous 
problem, has its back pressure reduced 12 lbs. per sq. in. by means of a con- 
denser thereby increasing the m.e.p. to 36 lbs. per sq. in. Find its i.h.p., 
b.h.p. and mechanical efficiency, assuming the same friction horse power as 
in the previous problem. 

The addition of a condenser to this engine increased its power output by 
what per cent? 

6. A certain engine working on the Rankine cycle uses 20 lbs. of steam 
per i.h.p. hr. If the steam has an abs. pressure of 150 lbs. per sq. in. and a 
temp, of 458.5° while the exhaust pressure is 4 lbs. per sq. in. abs., find the 
heat supplied per i.h.p. min. and the thermal efficiency on i.h.p. 

7. If the engine of the previous problem has a mechanical efficiency of 
90 per cent, what is the thermal efficiency on b.h.p.? 



PROBLEMS 767 

8. Suppose an engine in which the mechanical efficiency is 85 per cent re- 
quires 3000 lbs. of steam per hr. when delivering loo h.p. If the steam has a 
pressure of 150 lbs. per sq. in. abs., and a quality of 98 per cent, find the heat 
required per b.h.p. min., and the thermal efficiency on the i.h.p. and on the 
b.h.p. The engine is working on the Rankine cycle, and has a back pressure 
of 2 lbs. per sq. in. abs. 

9. With the same engine delivering the same power as in the previous 
problem, find the same quantities if the steam required is 2400 lbs. per hr., 
the steam having a pressure of 150 lbs. per sq. in. abs. and 100 degrees of 
superheat. 

10. If a Diesel engine delivers 750 h.p. hrs. per bbl. of crude oil, find its 
thermal efficiency on b.h.p. A barrel of oil contains 336 lbs. and the calorific 
value of this oil is 18,500 B.t.u. per lb. 

11. An 8" X 12" air compressor, while running 200 r.p.m. gives an indi- 
cator card having an area of 2.7 sq. in. for the head end, and 3 sq. in. for the 
crank end. The length of each card is 3 in. Scale of the spring is 60 lbs. per 
in. The piston rod is i^ in. in diameter. Find the i.h.p. 

12. A Diesel engine uses 4 bbl. of crude oil per day of 24 hrs. (i bbl. = 
= 336 lbs.) The heating value of the oil is 18,000 B.t.u. per lb. If the me- 
chanical efificiency is 73 per cent and the thermal efficiency on b.h.p. is 28.3 
per cent find the i.h.p., b.h.p. and oil used per b.h.p. hr. for this engine. 

13. A i2,ooo-h.p. steam turbine requires 12.3 lbs. of steam per h.p. hr., 
when receiving steam having 100° of superheat and a pressure of 190 lbs. per 
sq. in. abs. The vacuum is 28 in., and the barometer stands at 30 in. 

(a) Find the cycle efficiency for this turbine assuming it to operate on the 
Clausius cycle, {b) Find the delivered thermal efficiency, (c) What portion 
of the theoretical work of the cycle is actually delivered by the turbine? 

14. With the same data as in the previous problem, find the actual amount 
of heat lost per min. in this turbine, in excess of that rejected by the ideal 
turbine operating under the same conditions. 

15. A certain steam engine rated at 500 h.p. gives a total consumption 
curve which is a straight line. The total consumption at \ of rated load is 
6250 lbs. of steam per hour while that at rated load is 14,000 lbs. per hour. 
Plot the total consumption and the water rate curves for this engine between 
zero and rated curves. 

CHAPTER XIV. 

1. Find the work done (in B.t.u.), the cycle efficiency and the water rate 
of an ideal turbine operating on the Clausius cycle with steam at a pressure 
of 130 lbs. per sq. in. abs. and 100° of superheat, while the back pressure is 
15 lbs. per sq. in. abs. 

2. Solve problem i using a back pressure of i lb. per sq. in. abs. By what 
per cent was the power of this ideal turbine increased by exhausting into a 
condenser? 

3. Solve problem l using steam of the same pressure but having a quality 
of unity at the beginning of adiabatic expansion. 

4. Discuss the results of the preceding problems, as to the effect of super- 
heat and vacuum on the ideal water rates. 

5. Find the net work of the cycle, the cycle efficiency, and the theoretical 
water rate of an ideal engine working on the Carnot cycle, for which the 
upper temperature is 344.4° and the lower is 193.22°. The pressure at the 
beginning of the adiabatic expansion is 25 lbs. per sq. in. abs. 

6. Solve the previous problem, with all the conditions as above, except 
that the steam at the beginning of adiabatic expansion is dry and saturated 
at 344.4° F. 

7. Given admission pressure = 130 lbs. per sq. in. abs., D = 100°, release 
press. = 25 lbs. per sq. in. abs., and back press. = 15 lbs. per sq. in. abs., find 
the theoretical work of the cycle, the cycle efficiency, and the theoretical 
water rate, of an engine operating on the Rankine cycle. 

8. Solve problem 7 when the engine receives dry saturated steam. 



768 HEAT-POWER ENGINEERING 

9. Suppose an engine is working on the feed pump cycle, receiving steam 
with an abs. press, of 130 lbs. per sq. in. and 100° of superheat. Find the 
cycle efficiency, the theoretical water rate and the actual water per i.h.p. hr. 
if the indicated thermal efficiency is 3 per cent. 

10. Solve problem 9, using dry saturated steam. 

11. An engine is working on the Rankine cycle at a pressure of 130 lbs. 
per sq. in. abs. and superheated 100°; release occurs at a pressure of 25 lbs. 
per sq. in. abs.; back pressure is 15 lbs. per sq. in. abs. Find the theoretical 
water rate and the cycle efficiency. Find the actual steam used per b.h.p. hr. 
and the delivered thermal efficiency if this engine requires 30,000 lbs. of 
steam per day of 10 hrs. when delivering 100 h.p. 

12. Given dry saturated steam having a temperature of 327.8°, and an 
exhaust temperature of 213°, find the net work of the cycle, the cycle effi- 
ciency, and the theoretical water rate of an engine working on the Carnot 
cycle. 

13. Solve problem 12 for the Clausius cycle. 

14. Solve problem 12 for the Rankine cycle, assuming release to occur 
when a temperature of 240.1° has been reached. 

15. Solve problem 12 for the feed pump cycle. 

16. Starting with the same A Qi and working between the same tempera- 
ture limits as in problem 12, find the net work of the cycle, the cycle efficiency 
and the theoretical water rate of an engine working on the Clausius cycle. 

17. Solve problem 16 for the Rankine cycle, the release temperature being 
240.1°. 

18. Solve problem 16 for the feed pump cycle. 

CHAPTER XV. 

1. An engine has a piston displacement of 0.2 cu. ft. If its clearance is 
10 per cent, and release takes place at 95 per cent of the stroke, find the 
weight of steam in the cylinder at release, the quality then being 70 per cent 
and the pressure 25 lbs. per sq. in. abs. 

2. Find the quality of steam at cut off in a cylinder in which the piston 
displacement is 0.1278 cu. ft., clearance 10 per cent, cut off 25 per cent, steam 
pressure at cut off 115 lbs. per sq. in. abs., and the weight of steam in the 
cylinder at cut off 0.012 lbs. 

3. Determine the quality or degree of superheat of the steam in an engine 
cylinder at cut off, its pressure then being 125 lbs. per sq. in. abs. and its weight 
0.013 lbs. The piston displacement is 0.13 cu. ft., clearance 10 per cent, and 
the cut off takes place at 30 per cent of the stroke. 

4. Find the weight of cushion steam in a 6" X 8" engine in which clearance 
is 15 per cent; compression begins at 15 per cent of the stroke; the back 
pressure is 14.7 lbs. per sq. in. abs., and the quality of the cushion steam at 
the beginning of compression is 95 per cent. Find the pressure and the qual- 
ity at the end of this compression, assuming it to be adiabatic. 

5. Suppose the compression in the previous problem is not adiabatic, but 
is such that the compression pressure is 30 lbs. per sq. in. abs., find the quality 
of the cushion steam at the end of the stroke. 

6. An 8" X 10" engine running 300 r.p.m. double acting, with cut off 
taking place at 15 per cent of the stroke, and at a pressure of 120 lbs. per sq. 
in. abs., requires 35 lbs. of steam per i.h.p. hr. The compression begins at 
40 per cent of the stroke with a quality of unity and a back pressure of 5 lbs. 
per sq. in. abs. Clearance = 10 per cent. 

If this engine delivers 27 h.p. and has a mechanical efficiency of 90 per cent, 
(a) Find the quality of steam at cut off. 

{b) If the quality of the steam at the throttle is unity and "wire drawing" 
amounts to 5 pounds, find the delivered thermal efficiency. 

7. For the previous problem, assume release to occur at 90 per cent of the 
stroke, with an abs. pressure of 30 lbs. per sq. in. What is the quality at this 
point? 



PROBLEMS 



769 



8. Assuming the expansion line for problem 6 to follow the law, PV = 
const. 

(a) Find the quality at 15, 20, 30, 40, 50, 65 and 90 per cent of the stroke. 
(Tabulate results.) 

{b) Draw the quality curve for this expansion. 

9. Suppose the engine in problem 6 had received steam with sufficient 
superheat to cause the quality at cut off to be 88 per cent, and that by means 
of a steam jacket the expansion line is made to follow the law, PV-'^- = const. 
Find the condition of the steam at release, which occurs at 90 per cent of the 
stroke. 

10. The thermometer in a throttling calorimeter shows a temp, of 223°, 
the manometer reads 0.73 in. of mercury; and the barometer stands at 29.92. 
Find the quality of the steam entering the calorimeter if its pressure is 110.3 
lbs. per sq. in. gauge. 

11. Supposing that the thermometer in the above calorimeter had read 
213°, all other readings being the same, what would be the quality? Discuss. 

12. If by connecting to a condenser we may reduce the calorimeter pressure 
until the mercury manometer indicates 15.62 in. below atmosphere, find the 
quality of the steam below which the instrument could not be used with 
steam pressure and atmospheric pressure the same as in problem 10. 

13. What pressure would you have to maintain in the calorimeter, in order 
to measure quality as low as 92 per cent, the steam pressure being 100 lbs. per 
sq. in. abs. and the degree of superheat in the calorimeter to be not less than 5°. 



CHAPTER XVI. 

Heck's formula for estimating cylinder condensation in cylinders which 
are not steam jacketed is 

Vat V pe 
where m = fraction of moisture in the steam at any point "a" during ex- 
pansion. 
N = r.p.m. 

„ _ nominal cyl. surface in sq. ft. 
nominal cyl. vol. in cu. ft. 
_ 24 48 ( where d = diam. of cyl. in inches. 
/ d \ and / = length of stroke in inches. 
p = abs. press, in lb. per sq. in. at point "a." 
_ total vol. up to point "a" 
piston displ. 
Tf = a special temperature function of the pressure and is obtained from 
the following table by taking the difference between the values of K corre- 
sponding to the highest and the lowest pressures occurring in the engine. 



p K 


P 


K 


P 


K 


P 


K 


P K 


P 


K 


I 175 


IS 


210 


SO 


269.5 


90 


321-5 


160 


389 


230 


441 


2 179 


20 


220 


ss 


277 


100 


332.5 


170 


397 


240 


447-5 


3 183 


25 


229 


60 


284 


no 


343 


180 


405 


250 


454 


4 186 


30 


238 


bS 


291 


120 


353 


190 


413 


260 


460.5 


6 191 


35 


246 


70 


297 -5 


130 


362. 5 


200 


420 


270 


467 


8 196 


40 


254 


75 


304 


140 


371-5 


210 


427 


280 


473 


10 200 


45 


262 


80 


310 


150 


380.5 


220 


434 


290 


479 



Note. — For more complete table see page 112, vol. i, " The Steam Engine," Heck. 

This formula is most applicable over a range of cut- off from 16 to 65 per cent of the stroke. 



770 HEAT-POWER ENGINEERING 

1. Find the quality at cut off by Heck's formula for the intermediate cyl- 
inder of a triple expansion engine having a diam. of lo in. and a stroke of 6 in., 
the speed being 402 r.p.m., cut-off press., 112.2; admission press., 130; and 
back press., 51 lbs. per sq. in. abs.; clearance, 10 per cent; cut off, 36.2 per cent. 
By test it was found that the actual quality at cut off was 85.7 per cent; find 
the per cent error by computing with the above formula. 

2. A 17" X 24" engine running 72 r.p.m. gives a card which shows the 
adm. press, to be 133 lbs.; exhaust press., 16.2; cut off, 98.8 lbs. per sq. in. abs. 
Cut oft" occurs at 18.6 per cent stroke and clearance is 9.9 per cent. Find the 
quality at cut off by Heck's formula and find the per«cent error if test shows 
the actual quality to be 72.9 per cent. 

3. An 8" X 10" engine running 320 r.p.m. has cut off at 12 per cent with 
a pressure of 140; admission press, is 145, and back press. 4 lbs. per sq. in. 
abs.; clearance is 10 per cent. If a test shows the quality at cut off to be 
59 per cent, find the per cent error in result obtained by Heck's formula. 

4. A certain engine requires 18 lbs. of steam per i.h.p. hour when using 
dry saturated steam, but when the steam is superheated 340° it requires only 
II lbs. per i.h.p. hour. 

The admission pressure is 150 lbs. per sq. in. abs. and the back pressure is 
I lb. in each case. Find: 

(a) The per cent saving in steam required when superheat is used. 

(b) The per cent saving in heat required when superheat is used. 

(c) The per cent saving in steam required for ideal Clausius cycle when 
superheat is used. 

(d) The per cent saving in heat required for ideal Clausius cycle when 
superheat is used. 

{e) The difference in the saving in heat required for the actual and the 
ideal engine. This difference is due mainly to what? 

5. An engine is supplied with dry saturated steam having an abs. pressure 
of 150 lbs. per sq. in. 

Back pressure is 5 lbs. per sq. in. abs., the exhaust steam being liquified in 
a surface condenser. 

When running without a steam jacket, the engine requires 20 lbs. of steam 
per i.h.p. hr. 

When running with a jacket, it was found the engine required 18 lbs. per 
i.h.p. hr. for the cylinder, and 2 lbs. per i.h.p. for the jacket. 

Supposing there is no loss of heat in returning the condensate from the 
jacket, or from the condenser to the boiler, and that the jacket pressure is 
maintained at 150 lbs. per sq. in. abs., 

(a) Find the heat required by the engine per i.h.p. hr. for each of the above 
cases. 

(b) Find the ind. thermal efficiency for each of the above cases. 

(c) Find the per cent saving in heat required per i.h.p. due to jacketing. 

6. An engine running without a steam jacket requires 15.5 lbs. of steam per 
i.h.p. hr., and when running with the steam jacket requires a total of 14 lbs. 
per i.h.p. hr. The steam required by the jacket is 18 per cent of the total. 

The admission press, and jacket press, are both 165 lbs. per sq. in. abs.; 
the steam admitted to them has a quality of unity. 

In each case the condensate from the condenser is returned to the boiler 
at a temp, of 202° F., but the condensate from the steam jacket is delivered 
to the boiler at a temp, of 302°. Neglecting all leakage: (a) Find the heat 
supplied by the boiler per i.h.p. hr. for each of the above cases, (b) Find the 
per cent saving in heat required due to jacketing. 

CHAPTER XIX. 

I. (a) Lay out a symmetrical valve seat, with width of exhaust cavity 
5 ins., of metal between exhaust cavity and port i^ ins., and of ports i j ins. 
(b) Draw in its central position an external valve having steam and exhaust 
laps respectively I j ins, and (negative) | in. for the head end, and i| ins. and 



PROBLEMS 771 

(positive) I in. for the crank end; thickness of metal I in. Dimension and 
label completely. 

2. Same as problem i, except for an internal valve. 

3. Construct a rectangular diagram of valve displacements for a valve 
having the dimensions given in problem i, the angle of advance being 32!° 
and throw 2j ins., (a) for the H.E.; {b) for the C.E. 

4. Same as problem 3, but for polar diagram of valve displacements. 

5. With data of problems i and 3, construct the Sweet diagram for both 
ends of valve and show: (a) the crank and piston positions for all the events; 
Q)) the angles of rotation of crank and eccentric for each of the periods; (c) the 
maximum openings to steam and exhaust; {d) the lead, {e) Construct an 
elliptical diagram from the Sweet diagram. 

6. Same as problem 5, except for Zeuner diagram. 

7. Same as problem 5, except for Bilgram diagram. 

8. Given cut-off | stroke, the amount of lead \ in., the maximum width of 
opening of the steam edge of the valve i\ ins., release 95 per cent of stroke 
for H.E. and 90 per cent for C.E. Determine, for both ends, the value of 
(a) the angle of advance, (b) throw, (c) steam lap, {d) exhaust lap, and {e) 
crank and piston positions for each event. 

9. In problems 5 to 8, find the true positions of the piston in its stroke for 
each crank position found, the length of connecting rod being 6 times the 
length of crank. Let the eccentric circle represent the crank circle. 

10. A swinging eccentric is pivoted diametrically opposite the crank at a 
distance of 8 ins. from the shaft center; the distance from pivot to eccentric 
center is 6| ins., the largest throw of the eccentric is 2| ins., the steam lap is 
1 1 ins. and the exhaust lap is I in. (a) Draw the path of the swinging eccen- 
tric as in Fig. 160. Locate three eccentric positions, and get the throws and 
angles of advance, {b) Draw the H.E. Bilgram diagram and show the corre- 
sponding positions of the steam and exhaust lap circles, (c) Determine the 
positions of the crank for all events. 

11. Same as problem 10, but using the Sweet diagram. 

12. Same as problem 10, but using the Zeuner diagram. 

13. Independent cut-off gear, (a) Draw the Bilgram diagram for the main 
valve to give release 90 per cent and compression 85 per cent of stroke, lead 
8 in., and maximum steam opening i| ins. (b) With same eccentric throw, 
and in position for o, J and f cut-off, draw the lap circles for a cut-off valve 
having i in. negative lap and riding on an independent stationary seat, 
(c) Show the positions of the eccentrics with respect to crank (on H.E. 
dead center) for each cut-off. (d) Plot a diagram of openings similar to 
Fig. 171. 

14. Meyer Valve Gear, (a) Data same as in problem 13 (a) for main 
valve, (b) With throw of cut-off eccentric 3 ins. and angle of advance 90°, 
construct the Bilgram diagram and draw the lap circles for the cut-off valve 
to give cut-off at o, J, |, and f strokes, (c) Show the positions of the eccen- 
trics with respect to the crank (on H.E. dead center). 

CHAPTER XX. 

Note. — In the following problems it is assumed that the engine is double 
acting unless otherwise stated. 

1. It is desired to build a simple engine to give 75 i.h.p. under the following 
conditions: 

Cut off at 20 per cent. 
Clearance = 10 per cent. 
Steam press. = 140 lbs. per sq. in. abs. 
Back press. = 2 lbs. per sq. in. abs. 
R.P.M. = 200. 
If the diagram factor for this type of engine is 0.9 find size of cylinder. 

2. Suppose it is desired to build an engine to give 50 i.h.p., under the 
following conditions: Cut off 25 per cent; Clearance 12 per cent.; Steam 



772 HEAT-POWER ENGINEERING 

press. = 150 lbs. per sq. in. abs.; Piston speed = 400 ft. per min.; Back press. 
= 16 lbs. per sq. in abs. If the diagram factor for this type of engine is 85 
per cent, find the diameter of the cylinder and select stroke and r.p.m. 

3. Supposing that the engine in problem i has cut offs occuring from 10 
to 50 per cent of stroke, find the i.h.p. for these extremes. 

4. Given an engine 18" X 24" running 120 r.p.m. Back press. = 2 lbs. per 
sq. in. abs; Clearance = 10 per cent; Cut off = 40 per cent ; Diagram factor 
= 85 per cent. Supposing the cut off to remain constant, find the i.h.p. 's 
corresponding to steam pressures of 50, 90 and 130 lbs. per sq. in. abs. 

5. Find the weight of dry steam which must be supplied per i.h.p. hour 
for each case of problem 4, assuming the quality at cut off to be 80 per cent. 
Assume compression pressure to be 30 lbs. abs. and that the steam is dry and 
saturated at the end of compression. 

6. A compound engine is to give 600 i.h.p. when using steam having an 
abs. press, of 150 lbs. per sq. in. and having a back press, of 2 lbs. per sq. in. abs. 
If the cylinder ratio is to be 4 and the total ratio of expansion 12, find the 
size of cylinders. The piston speed is to be 750 ft. per min. and the engine 
is to run 150 r.p.m. Take diagram factor as 0.8. 

7. An 8" X 16" X 12" engine has cut off in the high press, cylinder at i 
stroke, the admission pressure is 150 lbs. per sq. in. abs. and the back pressure 
is 2 lbs. per sq. in. abs. Assuming the expansion line to be hyperbolic and that 
there is no receiver drop, and that the clearance is zero, find: (a) The total 
ratio of expansion, (b) The receiver pressure, (c) The point of cut off in 
the low pressure cylinder, (d) The temperature range in each cylinder. 
'(e) The portion of the work done by each cylinder. (/) The maximum force 
exerted on each piston rod. 

Sketch the PV-diagram for this expansion marking the pressure at the end 
of the expansion in each cylinder, and the volume in terms of the volume at 
cut off in the high pressure cylinder. 

8. Assume the cut off in the high pressure cylinder of the above engine 
is now made to occur at 5 stroke, all- other conditions remaining the same, 
find the same quantities as called for above. 

9. Assume the above engine is now made to cut off at J stroke in the 
high pressure cylinder and at 37I per cent stroke in the low, thus causing a 
receiver drop, find this drop and all the quantities called for above. 

ID. With the data of the previous problem find what portion of the total 
theoretical work was lost by the receiver drop. 

II. With the result of the previous problem solve for the constant "K" 
used in equation 293 of the text. Then with this value of K find the total 
m.e.p. referred to the low pressure cylinder. Does this check results already 
obtained from problem 9? 

CHAPTER XXII. 

1. Determine the amount of work theoretically obtainable with a turbine 
per pound of steam admitted at a pressure of 150 lbs. per sq. in. and super- 
heated 100 degrees and expanded to a 28-inch vacuum, (a) by calculation, 
(b) by means of the T^-chart, and (c) by means of the Mollier Chart. _ 

2. Same as problem i except that the exhaust pressure is atmospheric. 

3. Determine the amount of work theoretically obtainable with a turbine 
per pound of dry saturated steam at a pressure of 150 lbs. per sq. in. and 
exhausting into a 28-inch vacuum. 

4. Same as problem 3, except that the exhaust pressure is atmospheric. 

5. Plot a curve showing the variation in the amount of work obtainable per 
pound of steam used in a turbine with initial conditions varying from dry and 
saturated at 175 lbs. per sq. in. pressure to a superheat of 150 degrees above 
the temperature of saturation, the turbine exhausting into a 28-inch vacuum 
in every case. 

6. Plot a curve showing the variation in the amount of work obtainable 
per pound of steam used in a turbine with initial conditions constant at 150 



PROBLEMS 773 

degrees superheat and 175 lbs. per sq. in. pressure but with exhaust condi- 
tions varying from atmospheric pressure to a vacuum of 29 inches. 

7. Determine the theoretical water rate of a turbine operating under the 
conditions specified in problem i. 

8. Determine the theoretical water rate of a turbine operating under the 
conditions specified in problem 2. 

9. Determine the theoretical water rate of a turbine operating under the 
conditions specified in problem 3. 

10. Determine the theoretical water rate of a turbine operating under the 
conditions specified in problem 4. 

11. The over-all efficiency of a certain turbo-generator unit is 0.67 when 
receiving steam at a pressure of 175 lbs. per sq. in. superheated 125 degrees 
and exfcausting to a 28.5-inch vacuum. What is the water rate of the unit 
per k.w. hour? 

12. If the generator efficiency for the unit in problem 11 be 94 per cent, 
what is the water rate of the turbine per d.h.p. hour? 

13. Find the B.t.u. supplied per k.w. minute for the unit described in 
problem 11. 

14. Find the thermal efficiency of the unit described in problem 11. 

15. Assume a reciprocating engine to consume twenty pounds of steam per 
h.p. hour when exhausting at atmospheric pressure. How much work could 
theoretically be obtained from an exhaust steam turbine receiving this steam 
at a quality of 80 per cent and expanding to a 27.5-inch vacuum? 

16. Find the theoretical velocity of the jet in an impulse turbine receiving 
steam at a pressure of 100 lbs. per sq. in. with a superheat of 100 degrees and 
expanding to atmospheric pressure. 

17. Find the theoretical kinetic energy of the jet per pound of steam dis- 
charged in problem 16. 

CHAPTER XXVI. 

1. Plot a curve showing the variation of the theoretical efficiency of the 
Otto cycle due to changes in the compression ratio [(volume of piston dis- 
placement + clearance) -r- clearance volume] from 3 to 10 and with 7 = 1.4. 

2. Plot a similar curve for y = 1.33. 

3. A certain internal combustion engine operating on natural gas uses 10.3 
cu. ft. of gas per b.h.p. hour at rated load. The calorific value of the gas is 
1050 B.t.u. per cu. ft. (a) How many B.t.u. are required per b.h.p. per hour 
at rated load? {b) What is the thermal efficiency at rated load? (c) What 
values of thermal efficiency would you expect at half and quarter loads? 
Give method used in arriving at answer. 

4. A certain producer-gas plant delivers a b.h.p. per hour on one pound of 
coal, the calorific value of the coal being 13,500 B.t.u. per pound. What is 
the thermal efficiency of the plant? 

CHAPTER XXVII. 

1. The proximate analysis of coal as received is moisture, 7 per cent; vola- 
tile, 4 per cent; fixed carbon, 81 per cent; ash, 8 per cent, (a) What would 
be the proximate analysis on a basis of dry coal? {b) What would be the 
proximate analysis on a basis of dry combustible? 

2. The proximate analysis of coal as received is moisture, 10 per cent; 
volatile, 30 per cent; fixed carbon, 50 per cent; ash, 10 per cent, (a) What 
would be the proximate analysis on the basis of dry coal? {b) What would 
be the proximate analysis on the basis of dry combustible? 

3. The proximate analysis of a certain coal on the basis of dry coal is vola- 
tile, 20 per cent; fixed carbon, 70 per cent; ash, 10 per cent. What would 
be the proximate analysis of this fuel when containing 10 per cent moisture? 

4. The proximate analysis of a certain coal on the basis of dry combus- 
tible is volatile matter, 34 per cent; fixed carbon, 66 per cent, (a) What 
would be the proximate analysis of this fuel on the basis of dry fuel when 



774 HEAT-POWER ENGINEERING 

containing 8 per cent ash? (b) What would be the proximate analysis 
of this fuel as received when containing 8 per cent ash and 12 per cent 
moisture? 

5. Determine the probable ultimate analysis of an anthracite coal giving 
the following proximate analysis: volatile, 4 per cent; fixed carbon, 96 per 
cent. 

6. Determine the probable ultimate analysis of an anthracite coal giving 
the following proximate analysis: volatile, 3.5 per cent; fixed carbon, 90 per 
cent; ash, 6.5 per cent. 

7. Determine the probable ultimate analysis of a bituminous coal giving 
the following proximate analysis: volatile, 25 per cent; fixed carbon, 75 per 
cent. 

8. Determine the probable calorific values of the coal of problem 5 by means 
of Dulong's formulas. 

9. Same as 8, but for the coal of problem 6. 

10. Same as 8, but for the coal of problem 7. 

11. Determine the probable higher calorific value of a petroleum distillate 
with a specific gravity indicated as 95 on the Baume scale. 

12. Same as 11, except for a specific gravity of 85 Baume. 

13. Same as 11, except for a specific gravity of 75 Baume. 

14. Plot a curve showing the probable variation of higher calorific values 
of petroleum products with specific gravities varying from 50 to 95 Baume. 

CHAPTER XXVIII. 

1. What weight of oxygen will be required to burn 5 lbs. of carbon to car- 
bon dioxide? What weight of air will be required? How much nitrogen 
will there be in this air? 

2. What weight of oxygen will be required to burn 7^ lbs. of carbon to 
carbon monoxide? What weight of air will be required? What weight of 
nitrogen will be contained in this air? 

3. What weight of carbon dioxide will result from the combustion of 12 
lbs of carbon? What would be the total weight of the products of combus- 
tion (all material present after combustion) if the carbon were burned with 
the theoretical air supply? 

4. Seven pounds of carbon are burned with air to carbon monoxide, (a) 
What weight of carbon monoxide is formed? (b) What is the total weight 
of the products of combustion? 

5. Fifteen pounds of carbon are burned in oxygen to carbon dioxide. 
(a) What weight of carbon dioxide results? {b) How much heat is liberated? 
(c) How much heat would have been liberated if the combustion had taken 
place in air instead of in oxygen? 

6. Seventeen pounds of carbon are burned to carbon dioxide in an appa- 
ratus which makes it possible to complete the combustion in one second, and an 
equal quantity is burned to the dioxide in an apparatus which requires one 
hour to complete the combustion. Is there any difference in the amount of 
heat liberated in the two cases? Why? 

7. Three pounds of carbon are burned in air to carbon dioxide, (a) What 
will be the weight of the products of combustion if twice the theoretical 
quantity of air is used? (&) What will be the quantity of heat liberated? 

8. Four pounds of carbon are burned in air to carbon monoxide, (a) 
What will be the v/eight of the products of combustion? (b) What will be 
the quantity of heat liberated? 

9. A quantity of carbon monoxide containing 3 lbs. of carbon is burned 
with theoretical air supply to carbon dioxide, (a) What will be the weight 
of the products? (b) What quantity of heat will be liberated? 

10. Ten pounds of carbon monoxide are burned with ij times the theo- 
retical air supply, (a) What will be the weight of the products? (b) What 
quantity of heat will be liberated? 



PROBLEMS 775 

11. Twelve pounds of carbon are burned first to carbon monoxide with the 
theoretical quantity of air and then the resultant carbon monoxide is burned 
with I J times the theoretical air. (a) What weight of carbon monoxide is 
formed by the first reaction? (6) What is the total weight of gas after the 
first reaction? (c) What quantity of heat is liberated during the first reac- 
tion? {d) What weight of carbon dioxide is formed by the second reaction? 
(e) What is the total weight of gas present after completion of second re- 
action if no gas is lost during either reaction nor between reactions? (/) 
What quantity of heat is liberated during the second combustion? (g) What 
is the total quantity of heat liberated as result of both reactions and how 
does this compare with what would have been obtained had the 12 lbs. of 
carbon been burned directly to carbon dioxide? (h) How does the weight 
of products obtained by using two reactions compare with the weight that 
would have been obtained by burning directly to the dioxide with ij times 
theoretical air? 

12. Eight pounds of carbon are burned with air containing sufficient oxy- 
gen to burn 7 lbs. of carbon to carbon dioxide, (a) What are the weights 
of the various products of combustion? {b) What is the percentage compo- 
sition of the products of combustion on a volume basis? {c) What quantity 
of heat is liberated? 

13. The analysis of the gases obtained by burning carbon in air shows 
15 per cent by volume of carbon dioxide, (a) What is the excess coefificient? 
{b) How many pounds of air were used per pound of carbon burned? 

14. The analysis of gases obtained by burning carbon in air gives 79 per 
cent nitrogen and 7 per cent oxygen. (a) What is the excess coefficient? 
(6) What weight of air was used per pound of carbon? 

15. Five pounds of carbon are burned in air with an excess of 50 per cent, 
the combustion taking place at constant pressure, (a) What temperature 
rise will result? {b) What will be the final temperature if all material is at 
temperature of 70" F. before the start of the combustion? 

16. Sixteen cubic feet of carbon monoxide are burned with the theoretical 
quantity of oxygen within a vessel of constant volume. What temperature 
would be attained theoretically if the gases had an initial temperature of 
60° F.? 

17. What temperature would calculation lead one to expect when account 
is taken of the variable specific heat of carbon dioxide? 

18. Three pounds of hydrogen are burned in oxygen, (a) How much 
heat is liberated? (&) What temperature should be obtained if the specific 
heats were constant and theoretical oxygen were used, combustion occurring 
at constant pressure? (c) What value should be attained with 25 per cent 
excess oxygen, variable specific heat and constant pressure? 

19. What quantity of heat would be lost by failure to condense the water 
vapor resulting from the combustion of 3 lbs. of hydrogen if the gases leave 
at a temperature of 250° F. and room temperature is 60° F.? 

20. Determine the approximate higher and lower heat values by Dulong's 
formulas for a fuel of the following composition by weight: carbon, 70 per 
cent; hydrogen, 25 per cent; oxygen, 2 per cent; sulphur, 3 per cent. 

21. Determine the weight of dry fuel gases per pound of carbon burned 
for a case in which the gases analyze: carbon dioxide, 14 per cent; carbon 
monoxide, 2 per cent; hydrogen, i per cent; sulphur dioxide, i per cent; 
oxygen, 2 per cent; nitrogen, 80 per cent. 

CHAPTER XXX. 

1. During the test of a certain boiler it is found that when fired with coal 
with a heat value of 14,000 B.t.u. per pound the ash contains 0.2 of a pound 
of carbon per pound of coal fired, (a) What is the heat value of the ascend- 
ing combustible per pound of carbon? {b) What is the grate efficiency? 

2. If each pound of coal fired as in problem i causes the generation of 
8 lbs. of dry and saturated steam at a pressure of 150 lbs. abs. from feed 



776 HEAT-POWER ENGINEERING 

water at a temperature of 120° F., what is the value of the boiler efficiency 
according to the A.S.M.E. definition? 

3. What is the over-all efficiency of the boiler considered in problems i 
and 2 above? 

4. If a boiler generates 9 lbs of steam with a quality of 97 per cent at a 
pressure of 125 lbs. abs. from feed at a temperature of 70° F., what is the 
equivalent evaporation? 

5. A certain boiler generates steam at a pressure of 160 lbs. abs., and 
superheated 100 degrees from feed at a temperature of 200° F. What is the 
factor of evaporation? 

6. How many pounds of water at a temperature of 70° F. should be con- 
verted into dry saturated steam at 125 lbs gauge per hour by a loo-h.p. boiler 
when operating at normal load? What is the factor of evaporation for this 
case? How many pounds of material would leave the boiler per hour if it 
gave steam with a quality of 97 per cent? 

CHAPTER XXXII. 

1. (a) Using Fig. 326 and Table XXIV, how much draft through the 
boiler will probably be required to burn 20 lbs. of anthracite pea coal per 
square foot of grate per hour? {b) With 50 ft. of flue and two 90° bends, what 
will be the draft probably required at the base of the stack? 

2. (a) With fine temperature 550° F. and air at 60°, what would be the 
theoretical height of stack for case given in problem i? (b) What would be 
the actual height? (c) What would be its diameter in inches for a 2000 
boiler h.p. plant? 

CHAPTER XXXV. 

1. Determine the quantity of heat which will flow per hour between two 
planes i ft. apart and of 6 sq. ins. section with a temperature difference of 
100° F., the material being commercial copper and no allowance being made 
for variation of specific conductivity with temperature. Determine the 
"heat resistance" of the material between the two planes. 

2. Determine the same quantities as called for in problem i, but for a 
case in which soft steel is the conducting material. 

3. Determine the same quantities as called for in problem i, but for cases 
in which water and air are the conducting materials. 

4. Tabulate the values obtained for quantity of heat transmitted in above 
cases and tabulate values as percentage by calling that transmitted by copper 
100 per cent. 

5. Taking values from Table XXVI, determine the specific conductivity of 
yellow brass at a temperature of 200° F. 

6. Assuming values given in the text as correct, determine the amount of 
heat lost by radiation in i hour from the black surface of a sphere of i ft. 
radius and at a temperature of 1000° F. Do the same for a temperature of 
2000° F. 

7. (a) If the temperature difference at end a of the heating surface is 
2000° and at end b it is 200°, what is the mean temperature difference with 
flow? (b) li K = 3.7, how many square feet of heating surface will be re- 
quired to transmit per hour 33,463 B.t.u. (= i boiler h.p.)? 

8. A surface condenser receives exhaust steam at temperature 115° F., 
the initial temperature of the condensing water is 60° F. and its final temper- 
ature 105° F. (a) What is the mean tenperature difference? (b) With 
K = 300, what weight of dry steam will be condensed per square foot of sur- 
face per hour? (c) What is the efficiency of the surface (neglecting losses)? 

9. In a boiler the furnace gases are cooled from 2500° F. to 550° F. and the 
temperature of the steam is 350° F. (a) Neglecting losses, what is the mean 
temperature difference? (b) If 3^ lbs. of steam from and at 212° is evapo- 
rated per square foot of heating surface, what is the value of K? 



PROBLEMS 'J'J'] 

10. With parallel flow the initial and final temperature differences are 
500° and 203. (o) What is the mean temperature difference? {b) With 
^ = 3 B.t.u. how much heating surface is required for heating 30 lbs. of water 
per hour from 60° to 192°? 

11. (a) With counter-current flow, with a temperature difference of 322° 
at one end of the heating surface and 357° at the other end, what is the mean 
temperature difference.'' {b) With K = 2> B.t.u. how much heating surface 
is required for heating 30 lbs. of water per hour from 60° to 192° F.? 

12. In a feed water heater 90 lbs. of water per hour are heated by i sq. ft. 
of heating surface, K being 220. (a) If the initial temperature difference da 
is 142°, what is the final value db, neglecting losses? {b) What is the effi- 
ciency? (c) Compute the efficiencies corresponding to different extents of 
surface and plot curve showing its variations. 

13. In a boiler the initial temperature difference between gas and water is 
2000° F. (a) If 10 sq. ft. are provided per boiler h.p. hour and K is 3.7, 
what will be the final temperature difference (neglecting losses) if 100 lbs. of 
flue gas (with Cp = 0.24) are generated per boiler h.p. hour? {b) What is the 
efficiency? (c) Compute the efficiencies corresponding to different extents 
of surface and plot curves showing its variation. 

14. In an economizer with parallel flow, iT = 3, Wc = 30, Wh = 100, 
Ca= 0.24, 5=4, Ta= 600, ta= 100. Find Oh, Tb and ^6. 

15. Same data as problem 14, but for counter flow, (a) Find da, db, Tb 
and ta. 

CHAPTER XXXVI. 

1. Determine the theoretical percentage of saving effected by supplying feed 
water at a temperature of 120° F. instead of 60° F. to a boiler generating dry 
saturated steam at a pressure of 150 lbs. abs. 

2. Determine the theoretical percentage of saving effected by supplying 
feed water at a temperature of 200° F. instead of 60° F. to a boiler generating 
dry saturated steam at a pressure of 150 lbs. abs. What is the percentage 
saving if the boiler superheats the steam ioo°? What is the actual amount 
of heat "saved" per pound of steam generated in each case? 

3. How many pounds of steam per pound of water heated will be required 
to raise the temperature of feed from 60° F to 190° F. in an open heater oper- 
ated at atmospheric pressure if the steam enters the heater at atmospheric 
pressure and with 100 per cent quality? How many will be required if the 
steam has a quality of 90 per cent? What weight of water will leave the 
heater in each case for every pound of water entering? 

4. What is the maximum possible weight of steam exhausted from an 
engine at atmospheric pressure and 85 per cent quality which could be uti- 
lized in an open feed heater if the feed water is to have its temperature raised 
from 50° F. to 200° F. and if the heater has an efficiency of 95 per cent? 

5. An economizer with counter flow receives flue gas at temperature of 
600°, and water at 60°. Thirty pounds of water are heated per hour by 100 
lbs. of gas (Cp = 0.24) through 4 sq. ft. of surface, K being 3. (a) Find the 
increase in the temperature of the feed water and (b) the decrease in the 
temperature of the flue gas. 

CHAPTER XXXVII. 

1. (a) In a direct-contact condenser how much condensing water per pound 
of steam will be required if the vacuum is 26 ins. and the condensing water is 
raised from 60° F. to within 10° of the temperature of the exhaust steam 
(-E/. = 0.9)? (b) How much is required with 28-in. "vacuum"? 

2. (a) Same as i except for surface condenser, the temperature of the con- 
densate being reduced to 10° below that of the exhaust steam, (b) What is 
the mean temperature difference? (c) How much cooling surface is required 
per pound of steam condensed per hour ii K = 300? 



778 HEAT-POWER ENGINEERING 

3. If 400,000 lbs. of condensing water are used per hour in a jet condenser, 
what would be the probable plunger displacement in cubic feet per minute of 
a single-acting wet air pump? 

4. (a) If a surface condenser used with a turbine condenses 10,000 lbs. of 
steam per hour, what would be the probable plunger displacement of a wet- 
air pump in cubic feet per minute? (b) What, for a dry-air pump, the vacuum 
being 28 ins. Hg.? 

CHAPTER XL. 

I to 6. Same as problems 1-6 under Chap. XXII, except for nozzles. 

7. (a) Neglecting losses, find the discharge velocities per pound of steam 
flowing in problems i to 4. (b) Find the area of the nozzle end per pound of 
steam. 

8. With the initial conditions given in problems i to 4 plot curves as in 
Sec. 331. 

9. (a) If Ef. = 0.9, what heat remains per pound of steam at the end of 
expansion with the same conditions as in problems i to 4? (b) What is the 
final quality? (c) What is the final entropy? 

10. (a) Compute the neck areas in problem 8 by Napier's formula, (b) 
Same, by Grashof's formula. 

11. (a) With uniform fiow and allowing 5 lbs. drop in pressure, what 
would be the diameter of pipe to convey in i minute 200 lbs. of dry steam 
initially at 150 lbs. gauge pressure, the length of pipe being 200 ft.? (b) What 
would be the velocity of flow? 

12. (a) If a steam engine with cylinder 18 ins. diameter and stroke 24 ins. 
operates at 200 r.p.m., what should be the diameter of the steam pipe? (b) 
What should be the diameter of the exhaust pipe? 

14. (a) What weight of air will theoretically flow per second through a 
nozzle having a neck area of i sq. in., if the initial pressure is 80 lbs. per sq. 
in. abs. and temperature is 60° F. and if the discharge is into the atmosphere? 
(b) What will be the velocity of flow at the neck? 

15. (a) With initial pressure 20 lbs. per sq. in. abs. and temperature 60° F., 
what will be the theoretical velocity of discharge to the atmosphere? (b) 
What weight will flow per second through an orifice having an area of i sq. in.? 

16. With I lb. of air flowing through a nozzle per second with initial pres- 
sure (Pi) 80 lbs. per sq. in. abs. and temperature 60° F., plot curves showing 
how the decrease in back pressure (Px) affects (a) the velocity of flow, (&) the 
volume of the air and (c) the area of the nozzle, the abscissas being ratios 

Pl/Px. 

CHAPTER XLI. 

1. Determine the work which must be done per cycle in an air compressor 
cylinder without clearance which operates under the following ideal condi- 
tions. At the end of the suction stroke the cylinder contains one-tenth of a 
pound of air at a temperature of 60° F. and a pressure of 14.7 lbs. per sq. in. 
abs. 

2. Determine the work which must be done per cycle in an air compressor 
cylinder with clearance equal to 5 per cent of the piston displacement and 
which operates under the following conditions. It draws in one-tenth of a 
pound of air during the suction stroke; this air mixed with that caught in the 
clearance has a temperature of 60° F. at the end of the suction stroke; the 
pressure during the suction stroke is constant and equal to 14.7 lbs. per sq. in. 
abs.; compression and expansion are adiabatic; and air is discharged at a 
constant pressure of 50 lbs. per sq. in. abs. 

3. Determine the capacity of such a compressor in terms of free air (60° F. 
and 14.7 lbs.) per min. if it operates at a speed of 180 r.p.m. and is built 
double acting. 

4. Assume three compressor cylinders without clearance and with a piston 
displacement of i cu. ft., one cylinder so arranged as to give adiabatic com- 
pression; one arranged to give isothermal compression; and one arranged to 



PROBLEMS 779 

give a compression curve with exponent equal to 1.25. (a) Determine the 
work done during one compression in each cyUnder and the final temperature 
in each case if air with an initial temperature of 60° F. and at an initial pres- 
sure of 14.7 lbs. per sq. in. abs. is compressed to 45 lbs. per sq. in. abs. {b) 
Express the saving in the second and third cases as a percentage of the com- 
pression work in the case of the adiabatic process, (c) Determine the work 
per cycle in each case, assuming discharge to occur at the constant pressure of 
45 lbs. {d) Express savings as per cent, as in {b). (e) Make calculations 
called for in (a), (b), (c) and (d) but with a discharge pressure of 100 lbs. per 
sq. in. abs. 

5. Compare the work done in the air cylinder per cycle in the following 
cases, express saving as per cent of work in least favorable case, and deter- 
mine discharge temperature, (a) An air compressor cylinder without clear- 
ance has a diameter of 16 ins. and a stroke of 18 ins. The air at the end of 
the suction stroke has a temperature of 60° F., and a pressure of 14.7 lbs. per 
sq. in. abs. The compression is adiabatic and discharge occurs at a constant 
pressure of 100 lbs. per sq. in. abs. (b) The same cylinder with the same 
initial conditions gives a compression line with exponent equal to 1.3. (c) 
Two-stage compression is used with an intercooler. The low-pressure cylin- 
der has the same size as before and operates under the same initial conditions 
but gives a compression curve with exponent equal to 1.22 and discharges at 
such a pressure that cooling at constant pressure to initial temperature will 
give the air a volume equal to the piston displacement of the high-pressure 
cylinder. The high-pressure cylinder has a diameter of 10 ins. and a stroke 
of 18 ins., gives a compression curve with exponent equal to 1.22 and dis- 
charges at a constant pressure of 100 lbs. per sq. in. There are no transfer 
losses between stages. 

6. Assume that i lb of air with initial conditions 60° F. and 14.7 lbs. per 
sq. in. abs. has been compressed adiabatically to a pressure of 80 lbs. per sq. 
in., and then cooled at constant pressure to initial temperature after discharge 
from the compressor. If this air is used in an air engine without clearance, 
operating on a cycle of the same shape as the PV-diagram of the Clausius 
cycle, and expanding to atmospheric pressure, determine (a) the work made 
available in the engine, (b) the efficiency of the process in the ideal case, i.e., 
work made available -v- work done in air compressor cylinder, (c) The final 
temperature attained in the engine cylinder. 

7. Assume the same conditions as in problem 6 above, excepting that the 
air before entrance to the engine is preheated at constant pressure to a tem- 
perature of 300° F. Determine the values called for under (a), (b) and (c) of 
that problem. 



APPENDIX. 



USE OF COMMON LOGARITHMS FOR SPECIAL CASES. 

Case I. To Determine the «th Power of a Number 
Less than Unity. 

Example : Find 0.5^-^^ by logs. 

In general logio F'^ = nlogwV; and in this case V = 0.5 and 
n = 1.55- 

From the tables logio 0.5 = 9.6990 — 10, 

Then, 1.55 logio 0.5 = 1.55 (9.6990 - 10) = 15-033450 - 15-5 
Subtract 5.5 to reduce the negative part of 

the characteristic to 10, 5.5 — 5.5 

Log. of answer = 9.533450 — lo.o 
Corresponding number = 0.342 = 0.5^^^. 

(Note that a fraction raised to a power greater than unity 
gives a result less than the original fraction.) 

Case II. To Determine the wth Root of a Fraction. 
Example: Given V^'^ = 0.75; Find V. Evidently, — 

logio F= logio C^/075) = logio Vo-75^V = (logio 0.75) -^ 1.5, 
which is in the general form of logio F = (logio C) -r- n, 
where C = 0.75 and w = 1.5. 

From the tables logio 0.75 = 9-8751 — 10. 

Then MM5) ^ (9-8751 - 10) ^ _ ^ ^^^ 

1.5 1.5 ^ '^'^ 

Add 3.334 to raise the negative part 

of the characteristic to 10, 3-3340— 3-334 

Log. of F = 9.9173 — 10.000 

The corresponding number is 0.8266 which is ^'\/o.75. 

780 



APPENDIX 



781 





TABLE A. - 


- COMMON 


LOGARITHMS 


Logic) 






No. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 








0000 


3010 


4771 


6021 


6990 


7782 


8451 


9031 


9542 




10 


0000 


0043 


0086 


0128 


0170 


0212 


0253 


0294 


0334 


0374 


42 


II 


0414 


0453 


0492 


0531 


0569 


0607 


0645 


0682 


0719 


07S5 


38 


12 


0792 


0828 


0864 


0899 


0934 


0969 


1004 


1038 


1072 


1 106 


35 


' 13 


1 139 


1173 


1206 


1239 


1271 


1303 


1335 


1367 


1399 


1430 


32 


14 


146 1 


1492 


1523 


1553 


1584 


16 14 


1644 


1673 


1703 


1732 


30 


15 


1761 


1790 


1818 


1847 


1875 


1903 


1931 


1959 


1987 


2014 


28 


16 


2041 


2068 


2095 


2122 


2148 


2175 


2201 


2227 


2253 


2279 


26 


17 


2304 


2330 


235s 


2380 


2405 


2430 


2455 


2480 


2504 


2529 


25 


18 


2553 


2577 


2601 


2625 


2648 


2672 


269s 


2718 


2742 


2765 


24 


19 


2788 


2810 


2833 


2856 


2878 


2900 


2923 


2945 


2967 


2989 


22 


20 


3010 


3032 


3054 


3075 


3096 


3118 


3139 


3160 


3181 


3201 


21 


21 


3222 


3243 


3263 


3284 


3304 


3324 


3345 


3365 


3385 


3404 


20 


22 


3424 


3444 


3464 


3483 


3502 


3522 


3541 


3560 


3579 


3598 


19 


23 


3617 


3636 


3655 


3674 


3692 


3711 


3729 


3747 


3766 


3784 


19 


24 


3802 


3820 


3838 


3856 


3874 


3892 


3909 


3927 


3945 


► 3962 


18 


25 


3979 


3997 


4014 


4031 


4048 


4065 


4082 


4099 


4116 


4133 


17 


26 


4150 


4166 


4183 


4200 


4216 


4232 


4249 


4265 


4281 


4298 


16 


27 


4314 


4330 


4346 


4362 


4378 


4393 


4409 


4425 


4440 


4456 


16 


28 


4472 


4487 


4502 


4518 


4533 


4548 


4564 


4579 


4594 


4609 


15 


29 


4624 


4639 


4654 


4669 


4683 


4698 


4713 


4728 


4742 


4757 


15 


30 


4771 


4786 


4800 


4814 


4829 


4843 


4857 


4871 


4886 


4900 


14 


31 


4914 


4928 


4942 


4955 


4969 


4983 


4997 


5011 


5024 


5038 


14 


32 


5051 


5065 


5079 


5092 


5105 


5119 


5132 


5145 


5159 


5172 


13 


33 


5185 


5 198 


5211 


5224 


5237 


5250 


5263 


5276 


5289 


5302 


13 


34 


5315 


5328 


5340 


5353 


5366 


5378 


5391 


5403 


5416 


5428 


13 


35 


5441 


5453 


5465 


5478 


5490 


5502 


5514 


5527 


5539 


5551 


12 


36 


5563 


5575 


5587 


5599 


5611 


5623 


5635 


5647 


5658 


5670 


12 


37 


5682 


5694 


5705 


5717 


5729 


5740 


5752 


5763 


5775 


5786 


12 


38 


5798 


5809 


5821 


5832 


5843 


5855 


5866 


5877 


5888 


5899 


II 


39 


59" 


5922 


5933 


5944 


5955 


5966 


5977 


5988 


5999 


6010 


II 


40 


6021 


6031 


6042 


6053 


6064 


6075 


608s 


6096 


6107 


6117 


II 


41 


6128 


6138 


6149 


6160 


6170 


6180 


6191 


6201 


6212 


6222 


10 


42 


6232 


6243 


6253 


6263 


6274 


6284 


6294 


6304 


6314 


6325 


10 


43 


633s 


6345 


6355 


6365 


6375 


6385 


6395 


6405 


6415 


6425 


10 


44 


6435 


6444 


6454 


6464 


6474 


6484 


6493 


6503 


6513 


6522 


10 


45 


6532 


6542 


6551 


6561 


6571 


6580 


6590 


6599 


6609 


6618 


10 


46 


6628 


6637 


6646 


6656 


6665 


6675 


6684 


6693 


6702 


6712 


9 


47 


6721 


6730 


6739 


6749 


6758 


6767 


6776 


6785 


6794 


6803 


9 


48 


6812 


6821 


6830 


6839 


6848 


6857 


6866 


6875 


6884 


6893 


9 


49 


6902 


6911 


6920 


6928 


6937 


6946 


6955 


6964 


6972 


6981 


9 


50 


6990 


6998 


7007 


7016 


7024 


7033 


7042 


7050 


7059 


7067 


9 


51 


7076 


7084 


7093 


7101 


7110 


7118 


7126 


713s 


7143 


7152 


9 


52 


7160 


7168 


7177 


7185 


7193 


7202 


7210 


7218 


7226 


7235 


8 


53 


7243 


7251 


7259 


7267 


7275 


7284 


7292 


7300 


7308 


7316 


8 


54 


7324 


7332 


7340 


7348 


7356 


7364 


7372 


7380 


7388 


7396 


8 



y82 APPENDIX 

TABLE A. {Concluded). — COMMON LOGARITHMS (Logio). 



No. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


55 


7404 


7412 


7419 


7427 


7435 


7443 


7451 


7459 


7466 


7474 


8 


56 


7482 


7490 


7497 


750s 


7513 


7520 


7528 


7536 


7543 


7551 


8 


57 


7559 


7566 


7574 


7582 


7589 


7597 


7604 


7612 


7619 


7627 


8 


58 


7634 


7642 


7649 


7657 


7664 


7672 


7679 


7686 


7694 


7701 




59 


7709 


7716 


7723 


7731 


7738 


7745 


7752 


7760 


7767 


7774 




60 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 




61 


7853 


7860 


7868 


7875 


7882 


7889 


7896 


7903 


7910 


7917 




62 


7924 


7931 


7938 


7945 


7952 


7959 


7966 


7973 


7980 


7987 




63 


7993 


8000 


8007 


8014 


8021 


8028 


8035 


8041 


8048 


8055 




64 


8062 


8069 


8075 


8082 


8089 


8096 


8102 


8109 


8116 


8122 




65 


8129 


8136 


8142 


8149 


8156 


8162 


8169 


8176 


8182 


8189 




66 


8195 


8202 


8209 


8215 


8222 


8228 


8235 


8241 


8248 


8254 




67 


8261 


8267 


8274 


8280 


8287 


8293 


8299 


8306 


8312 


8319 


6 


68 


8325 


8331 


8338 


8344 


8351 


8357 


8363 


8370 


8376 


8382 


6 


69 


8388 


839s 


8401 


8407 


8414 


8420 


8426 


8432 


8439 


8445 


6 


70 


8451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 


8506 


6 


71 


8513 


8519 


8525 


8531 


8537 


8543 


8549 


8555 


8561 


8567 


6 


72 


8573 


8579 


8585 


8591 


8597 


8603 


8609 


8615 


8621 


8627 


6 


73 


8633 


8639 


8645 


8651 


8657 


8663 


8669 


8675 


8681 


8686 


6 


74 


8692 


8698 


8704 


8710 


8716 


8722 


8727 


8733 


8739 


8745 


6 


75 


8751 


8756 


8762 


8768 


8774 


8779 


8785 


8791 


8797 


8802 


6 


76 


8808 


8814 


8820 


8825 


8831 


8837 


8842 


8848 


8854 


8859 


6 


77 


8865 


8871 


8876 


8882 


8887 


8893 


8899 


8904 


8910 


8915 


6 


78 


8921 


8927 


8932 


8938 


8943 


8949 


8954 


8960 


8965 


8971 


6 


79 


8976 


8982 


8987 


8993 


8998 


9004 


9009 


9015 


9020 


9025 


5 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


5 


81 


9085 


9090 


9096 


9101 


9106 


9112 


9117 


9122 


9128 


9133 


5 


82 


9138 


9143 


9149 


9154 


9159 


9165 


9170 


9175 


9180 


9186 


5 


83 


9191 


9196 


9201 


9206 


9212 


9217 


9222 


9227 


9232 


9238 


5 


84 
85 


9243 


9248 


9253 


9258 


9263 


9269 


9274 


9279 


9284 


9289 


5 


9294 


9299 


9304 


9309 


9315 


9320 


9325 


9330 


9335 


9340 


5 


86 


9345 


9350 


9355 


9360 


9365 


9370 


9375 


9380 


9385 


9390 


5 


87 


9395 


9400 


9405 


9410 


9415 


9420 


9425 


9430 


9435 


9440 


5 


88 


9445 


9450 


9455 


9460 


9465 


9469 


9474 


9479 


9484 


9489 


5 


89 


9494 


9499 


9504 


9509 


9513 


9518 


9523 


9528 


9533 


9538 


5 


90 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


5 


91 


9590 


9595 


9600 


9605 


9609 


9614 


9619 


9624 


9628 


9633 


5 


92 


9638 


9643 


9647 


9652 


9657 


9661 


9666 


9671 


9675 


9680 


5 


93 


9685 


9689 


9694 


9699 


9703 


9708 


9713 


9717 


9722 


9727 


5 


94 


9731 


9736 


9741 


9745 


9750 


9754 


9759 


9763 


9768 


9773 


5 


95 


9777 


9782 


9786 


9791 


9795 


9800 


9805 


9809 


9814 


9818 


5 


96 


9823 


9827 


9832 


9836 


9841 


9845 


9850 


9854 


9859 


9863 


4 


97 


9868 


9872 


9877 


9881 


9886 


9890 


9894 


9899 


9903 


9908 


4 


98 


9912 


9917 


9921 


9926 


9930 


9934 


9939 


9943 


9948 


9952 


4 


99 


9956 


9961 


9965 


9969 


9974 


9978 


9983 


9987 


9991 


9996 


4 



Naperian log^ = 2.302 logio. 



APPENDIX 783 

TABLE B. — HYPERBOLIC OR NAPERIAN LOGARITHMS, (log,). 



N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


1. 00 


0.0000 


2.30 


0.8329 


3.60 


I . 2809 


4.90 


1.5892 


6.40 


1.8563 


105 


0.0488 


2-35 


0.8544 


3 


65 




2947 


4 


95 




5994 


6.50 


I. 8718 


1. 10 


0.0953 


2.40 


0.8755 


3 


70 




3083 


5 


00 




6094 


6.60 


I. 8871 


115 


0.1398 


2.45 


0.8961 


3 


75 




3218 


5 


05 




6194 


6.70 


I. 9021 


1.20 


0.1823 


2.50 


0.9163 


3 


80 




3350 


5 


10 




6292 


6.80 


I. 9169 


1-25 


0.2231 


2.5s 


0.9361 


3 


85 




3481 


5 


15 




6390 


6.90 


1-9315 


1.30 


0. 2624 


2.60 


0.9555 


3 


90 




3610 


5 


20 




6487 


7.00 


1-9459 


1-35 


0.3001 


2.65 


0.9746 


3 


95 




3737 


5 


25 




6582 


7.20 


I. 9741 


1 .40 


0.3365 


2.70 


0.9933 


4 


00 




3863 


5 


30 




6677 


7.40 


2 . 0015 


1-45 


0.3716 


2.75 


I. 01 16 


4 


OS 




3987 


5 


35 




6771 


7.60 


2.0281 


I-50 


0.405s 


2.80 


1 . 0296 


4 


10 




4110 


5 


40 




6864 


7.80 


2 . 0541 


1-55 


0.4383 


2.85 


I -0473 


4 


15 




4231 


5 


45 




6956 


8.00 


2.0794 


1.60 


0.4700 


2.90 


I . 0647 


4 


20 




4351 


5 


50 




7047 


8.25 


2. I 102 


1.65 


0.5008 


2-95 


I. 0818 


4 


25 




4469 


5 


55 




7138 


8.50 


2 . 1401 


1.70 


0.5306 


3.00 


1.0986 


4 


30 




4586 


5 


60 




7228 


8.75 


2.1691 


1-75 


0.5596 


3-05 


1.1151 


4 


35 




4702 


5 


65 




7317 


9.00 


2.1972 


1.80 


0.5878 


3-IO 


1.1314 


4 


40 




4816 


5 


70 




7405 


9-25 


2.2246 


1.85 


0.6152 


31S 


I . 1474 


4 


45 




4929 


5 


75 




7492 


9 50 


2.2513 


1.90 


0.6419 


3.20 


I. 1632 


4 


50 




5041 


5 


80 




7579 


9-75 


2.2773 


1-95 


0.6678 


3-25 


I. 1787 


4 


55 




5151 


5 


85 




7664 


10.00 


2.3026 


2.00 


0.6931 


3.30 


I • 1939 


4 


60 




5261 


5 


90 




7750 


11.00 


2.3979 


2.05 


0.7178 


3-35 


I . 2090 


4 


65 




5369 


5 


95 




7834 


12.00 


2 . 4849 


2.10 


0.7419 


3-40 


1.2238 


4 


70 




5476 


6 


00 




7918 


13.00 


2 . 5649 


2.15 


0.7655 


3-45 


I . 2384 


4 


7S 




5581 


6 


10 




8083 


14.00 


2.6391 


2.20 


0.7885 


3-50 


1.2528 


4 


80 




5686 


6 


20 




8245 


15.00 


2.7081 


2.25 


0.8109 


3-55 


I . 2669 


4.85 


I -5790 


6.30 


I ; 8405 


16.00 


2.7726 



(i) To find loge of a number greater than 10 (for example 21): — 

Loge2I = loge (lO X 2.l) = loge lO + logg 2.1 = 2.3026 + O.7419 = 3.O445. 

(2) Base e = 2.71828 and loge a = 2.302 X logioc. 



784 



APPENDIX 



B . 

I 



•5 '2^ 



ax! «i 



CD-* "j 
.2 3 « 



^E' 



-CX) 






3gK 



^w3 

III 

ell 



§ s : - 



s^a 



g^3^ 



O 






M (S rO'+lO 



O O O CA O^ 1 



ro O t^ >0 Tj- 



to cv^jOO O ro 



loo fr) -^ O -^O On' 

•^ Lovo <N f^ CO rO t^ 1 

^OO * M OO NO -* <N I 

OvOO 00 CO I^ J^ r^ f- 1 



ooooo ooooo 



o o o o o 









Tt-OO i^nO 00 >ONO ro lOOO 

^ lO O t^ t-~ ro OnOD O^ O 

On CO O r^NO -^ CM M O O 

OOOOnOn OnO>OnOnOn 



Tt- O oo -* 
toco ^ w 

r^ " CO NO 
On OnOO 00 C 



M 0<NNONO-* Ot^tOl 



ro On M On 

NO NO NO NO NO 



On m 00 On rOCO •* O NO -^ w 

M OCOt^t^NO NONO>OlOlO 

O OOnO^OnOn OnOnOnOnOn 



I^ CO i-i 00 NO 

ooooo 



CO NO CO On •-* NO 



O NO lO LO 



I O <N 
to <N 



(S CO 't »0 



+ 1 + 1 
O O O o 



I ++++ 



CO CO •* ■* 



APPENDIX 



785 





M t/5 

53 


6. 


a. 


^ t^oo o\ iH <s <n •* 




If? ^^«^S SSf?^!? 


4i 


3; 
> 


^^^T^'^ 2^5=8 


On 


^ S"^^ ^'S 'S ^nS ss> 




NO 


NO rt ro <N M Onoo r^NO NO 


1 


a 

> 


1 


VO lO LO U-) 10 Tt Tt Tt rt 


^ 
"+ 


NO M in t^xjiiT) i^^monOtC 
^ CO^WO^ 0000 r^NO NO 
















i 


r-t^i>.ioco OvOMOO 
Tj- io\o r^oo Ov ON 


CO 
!NO 


ro 00 -N t^ M lo On r^NO On ^O 
CO ro^O^OfOco cocOro^Oro 


00000 0000 





00000 00000 


3 
e5 


-e- 
< 


OOvOlfJtOt^ ONtsoO 
<N M 000 C^ f^O MO 


NO 


On '^ThOOO OMrt- ONNO 
^ On^OnOCS OOt^OnOco 














CO 

•a 

!=) 

2 

1 

< 


1 


03 

n 
u 


3 


00 Tt VO w TfOO IN MD 


00 


On <N 1000 <N T^ t^ On IN 




- 


04 rororo^-* '^J-Tt'^'Oin 


'3 
1 


a. 


Orhoi^Ov OOOOOro 


NO 


00 ^ H OnOO 00 On <N 1000 


rqc^HMH 0000» 
0^ On ON ON On OnOO 


1^ 


NO x+iNO>r-iO pomOoono 
00 00 CO 00 00 00 00 00 00 <^C» 


13 



3 


0000<NOO (NVOCSOn 


^ 


t^ NO NO t-00 ro r^ M 10 


lO M 00 10 <N OnnO Tf H 
ONO^O^ONON OnOnOnOn 




ON 


On t^iOOOMO 00NOlOr-0!N 

NO NO NO NO NO lO 10 10 LO to 

On On On On On On On On On On On 




a* 


0< r^oo <N i-i t^ Onoo 10 


8 


^ 10 »o Ti- i-i 00 roco w rf 


r^^ONOM loONtvjt^ 
ro ^ LO 100 NO ^ t>. t^ 


eg 


00 oo<»ononon onOo'oo 













t^LOOMlH OvlOOn- 


■* 


r>. Omc^<ncn) mOoonO'"^ 


rONO On w ro n-NO 00 ON 


0^ 


CN CO Tf- lONO t^OO 00 On 
10 ly^loLolOlO UOIOIO lONO 




'-' 


„ MHMMM MHMMM 




- 


00 00 CN (N r-. Onoo ^ 


8 


cO'*T^'^)0 NOW tooo w 


ONO<Nootr> r^MioON 
r^ r^oo 00 0\ On 


H 


CO NO On <N 1000 CO to r^ 
H HMCscscN) cocococo^ 


1 
1 


ir: 


0. 


NO t^OO Oi M M fO ■>*• 


■<*■ 


in NO t>.00 0\ M N ro TflO 


i 








^0 


CO cococococo cococococo 
H (nJ r^j 4 x^ ^' t-L(xj (^ 



786 



APPENDIX 



1^3 




o. 


^^<?5^s, 


%;^^^^ 


tT 5 Tl- rt in 


as^^sg 


^n 


> 


?L=S^^S 


S^^5? 


CN OS O -* M 
O lO IN 00 LO 


O M lo o r^ 

IN OsO -^ M 


>0 to T^ Tj- CO 


O) 0) M M O 


O OS Osoo 00 


00 t-. t- r^ t^ 








o 


i 


X 


o) CV5 lo r^ H 

^CO MOW 


lO t^ "* lO 1-1 
O O H cs rt 
CS M O OsOO 
CO CO CO o. CN 


OS H t^so CO 
lOOO O coo 

t^o o >o •* 


oi Osoo 00 O 






"3 


< 


-^ -* ro oi O 

>p ON r^ -oog 

ro CO CO ro ro 


CO -+ IN t^ O 

COOO CO t^ cs 
r^ l^OO 00 On 
CO CO CO CO CO 


t^ ^ -* -nT ■* 


1^ O o) c^ oi 

^ ^ ^ ^ ^ 


o o o o o 


o o o o o 


o o o o o 


o o o o o 


O 
H 


? 

5 


r^ i^ r^ t^iO 


00 H VO CS M 


II CO f^ CO H 
C^ 00 ^ 1-1 OO 

r^O O so Lo 

O O O so o 


OS OS O O M 

Tf 1-1 OsO CO 

O so o o o 






a 

2 

1 




C 
u 

1 




lO t^OO 0\ M 


CO r^ Os !N rt 


O Os O IN lr> 


O CO Os 1-1 CO 


lO LO lo too 
t^ t^ r^ r^ t^ 


so so so t^ f- 


1^ t^co CO 00 
r^ r^ t^ r^ j^ 


00 00 OO OS OS 
t^ f^ r- r^ r^ 


s 

G 


a. 


M lo O lo O 


<N Ti-00 CO OS 


O CO cs M 


M 1-1 CO ^O 


lO ro O) O O 
t^ !>. 1^ r^O 

CO OO 00 OO 00 


CO CO OO 00 00 


CO w OS t-^ "O 
»o lO -* ■* ■* 
00 OO OO 00 OO 


-;)■ 5- CO Si CO 
00 00 00 00 OO 


O 


3 


O <N 00 >+ M 


lOH t-.tOCO 


CS M (N CO lO 


r^ OS IN UO Os 


O On r^O lO 


HgSs 


H Os I^ >0 CO 

S Os OS OS Oi 


1-1 OSOO O ^ 
OS OS OS OS OS 


1 


5 


O 1^00 00 00 


so (N so Os M 


H O OO lO H 


O w lOOO H 


O IN Tt^ OO 


S^ S^^|, 


Os oi ^ r^ O 
CO ^ ■* ^ lo 


oi lo r- OS M 

lO lO VO lJ-)0 


3 
(2 


§ 


CS OO IN OS 


w CO CO Tt rj- 


CO w O 00 ^O 


CO O r^ -* O 


M M IN ro CO 

o vo so >o o 


s^S^S^ 


S- ^S- S-5 


^ lo too r^ 
r^ t^ r^ r^ t^ 






- 


<N 1^ •+ -:!- CO 


M so O CS CO 


IN H OO lO O 


lO Os ^ lot-. 


CN 'A-O OO O 




O CO looo 1-1 
t^ :^ t^ r^co 


CO lOOO O <s) 
00 CO OO Os 0^ 


i 


CO 


Q< 


^Jr^^si 


ro rO fO fO ■* 


i^^^-^S) 


aiS^^Ng 


CD 6 
* PL, 




CO rO CO CO ro 


CO CO CO CO CO 


COl CO CO CO CO 


CO CO CO CO CO 


H C) CO Tt >0 


r^ OS w coio 


r^ OS M CO >o 

OJ (N CO CO CO 


t~, Os H CO lO 
CO CO Tt rl- -^ 



APPENDIX 



787 







o, 


^.^SSR 


fi^^^cg 


^^s§8a 


s.3;^<§.§ 


'il 


> 


>0 lOMO 00 O 
O t^ lO ro C^ 


T|- On ^ O t-~ 

CO r-NO -* 


^?:28^ 


SnE^^ ^ % 


\0 O O y3 O 


NO to to to to 


to to... 


. ■=!- Tl- . M- 


1 


a 

> ■ 


3^ 


sHH 


00 w to O to 

-^ O uo M NO 
00 CO r^ r-NO 


CO M O O M 

c^ OO . O NO 
NO to to to -* 


CO tooo « t^ 

Tj- CO CO !o CN 








'3 
cr 


1 


o) O 00 lo H 
fO looo i-i 
CO ro CO CO -^ 
^ '^ '^ -^ ^ 


^ -* ^ ^ ^ 


t^ On H CO -^t 




O O o 


O O O o 


O O O O 


o o o o o 


o 


^ 

? 


00 lo ^ 

o o o o o 


to CO oj M O 
00 NO ■* w O 

NO NO NO NO O 


O O w CO to 
00 NO ■* c^ O 

NO NO NO NO NO 








•a 

•+3 


1 


1 


i 


Tl-vO t^OO On 


O Ol CO ^ to 


NO 1^00 On On 


O H 0) CO 'Ij- 


On 0> ON ON On 
j~~ r-~ r^ r^ t-~ 


O O O O 

00 CO CO 00 00 


O O O 

CO OO CO CO CO 


00 00 00 00 c» 


'cd 


a. 


ON IN lO On CO 


00 w t^ coco 


-^i- o NO CO o 


t^ Ti- w OnnO 


CO CN OO t^ 
CO CO CO Ol <N 

00 CO 00 CX) 00 


J^ ^ ^ ^ On 

cS M c3 cS 00 


00 r^ to Tl- CO 

CO CO GO 00 CO 


00 00 OO 00 00 


-2 


5 


coco (N r^ C) 


00 -* O r^ CO 


O r^ '^ CN ON 


r-to CO c) O 


CO M O CO 1>. 
M M M o 
On On On On ON 


O^ ^ O O 8 

On ON On On ON 


On r^NO to CO 
On On On On On 
00 OO 00 00 OO 


On on OnOo'oO 

00 CO 00 CO 00 


^ 
cS 

^ 


5^ 

a* 


CO ^ lONO NO 


toi to CO CM O 


00 to CS On to 


H t^ COOO CO 


ms-s- 


TJ-NO 00 O Ol 


CO to r^oo O 

00 00 OO 00 On 


CN) CO tONO 00 


3 


g 


NO <N 00 COOO 


'^t- On ^00 CO 


00 c^ NO o . 


00 w NO O CO 


t^OO CO On On 


O O w M (N 

OO 00 00 CO CO 


c^ CO CO ■* <* 

00 00 00 OO 00 


-:!- to tONO NO 
00 00 00 00 00 






- 


On O O O On 


00 t-~ to CO 


00 -^ M C^ CO 


OO . On tJ-OO 


■^ (^ On l-H <N 
On On On O O 


CO CO CO CO CO 


CO to r-00 O 

CO CO CO ^ CO 


M CO .NO t^ 
CO CO CO CO CO 


|3 


en wn 


a 


vg^^ggg. 


« ■<i-NO00 o 
1>1>J>1>00 


00 00 00 00 Ol 


SsS;^'§n8 


(U a3 
* Ah 


c 
6' 


CO CO CO CO CO 


CO CO CO CO CO 


CO CO CO CO CO 


CO CO c^ CO CO 


r^ On 1-1 CO to 
^ -^ to to lO 


r^ On M CO to 
to tONO NO NO 


r-» On w CO to 

NO NO t^ r^ t^ 


r^ On w CO to 
!>. t^C30 00 00 



788 



APPENDIX 



Pres. 
Abs. 

Lbs. 
Sq. In. 


o< 


sSsaa s'S^^s^ Sl^&^ '§<S2^§I 


^^d 


> 


^5^^^^ c;>^?22 s^i^^^s ^'^^%% 

<NOoOt^>o ^cocnmO OnOO t^O NO ID ■* Tt CO <N 
4 4 ro ro fO ro CO ro fO ro <N cs (N <N cN <N <N (N iN (N 


I 


i 

> 


T 


wooO^O On<nio<nO OnhnOhoo io->* ^hN© Os 
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APPENDIX 



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790 



APPENDIX 



TABLE D 
PROPERTIES OF ONE POUND OF 

SUPERHEATED STEAM. 

[Condensed from Marks and Davis's Steam Tables and Diagrams, igog, by permission of the 
publishers, Longmans, Green & Co.] 



Sp. V = specific volume in cu. ft. ; AQ 
Act) = total entropy above 32° F. 



B.t.u. total heat above 32° F. 



Absolute 

Pressure. 

Lbs. Sq. In. 








Degrees of Superhea 








Sat. Temp. 
°F. 


° 


50 


100 


150 


200 


250 


300 


^5 1 

(213) I 


Sp. V. 
A<2 
A4, 


26.27 
1150.7 
I ■ 7549 


28.40 
1174,2 
I . 7886 


30.46 
1197. 6 
I. 8199 


32.50 
1221.0 
1.8492 


34.53 
1244.4 
1.8768 


36.56 
1267.7 

I .9029 


38.58 
1291.1 
1.9276 


50 1 

(281) 1 


Sp. V. 
AQ 
A4> 


8. SI 
1173.6 
I. 6581 


9.19 
1198.8 
I . 6909 


9.84 
1223.4 
1.7211 


10.48 
1247.7 
I. 7491 


II . II 

1271.8 
1-7755 


11.74 
1295.8 

I . 8002 


12.36 
1319.7 
1.8237 


100 J 

(327.8)| 


Sp. V. 
AQ 
A<j) 


4-43 
1186.3 
1.6020 


4.79 
1213.8 
1.6358 


5-14 
1239.7 
1.6658 


5-47 
1264.7 
1-6933 


5-80 
1289.4 
I. 7188 


6.12 

1313.6 
1.7428 


6.44 
1337.8 
1.7656 


no 1 
(334. 8) 1 


Sp. V. 
AQ 


4.05 
1188.0 
1.5942 


4.38 
1215.9 
1.6282 


4.70 
1242.0 
1.6583 


S-oi 
1267. I 
1.6857 


5-31 
1291.9 
1.7110 


5.61 
1316.2 
1.7350 


590 
1340.4 
1.7576 


120 J 

(341. 3) 1 


Sp. V. 
AQ 
A<j> 


3-73 
1189.6 

1.5873 


4.04 
1217.9 
I. 6216 


4-33 
1244. I 
I. 6517 


4.62 
1269.3 
1.6789 


4.89 
1294. I 
I . 7041 


5.17 
1318.4 
1.7280 


5.44 
1342.7 
1.7505 


130 1 

(347.4)[ 


Sp. V. 
AQ 
A<t> 


3-45 
1191.0 
1.5807 


3-74 
1219.7 
1.6153 


4.02 
1246. I 
1.6453 


4.28 
1271.4 
1.6724 


4-54 
1296.2 
1.6976 


4.80 
1320.6 
I. 7213 


505 
1344.9 
1.7437 


140 j 

(353. i)| 


Sp. V. 

AQ 
A(j, 


3.22 
1192.2 
1-5747 


3-49 
1221.4 
I . 6096 


3-75 
1248.0 
1.6395 


4.00 

1273-3 
1.6666 


4.24 
1298.2 
I. 6916 


4.48 
1322.6 
1.7152 


4.71 
1346.9 
1.7376 


150 ( 

(358. 5) 1 


Sp.V. 
AQ 
A4> 


3.01 
II93-4 
1.5692 


3-27 
1223.0 
1.6043 


3.51 
1249.6 

I ■ 6343 


3-75 
1275. I 
I. 6612 


3.97 
1300.0 
1.6862 


4.19 
1324.5 
I . 7097 


4.41 
1348.8 
1.7320 


160 

(363.6) 


Sp.V. 
A<3 

A</> 


2.83 
1194.S 
I • 5693 


3.07 
1224.5 
1.5993 


3.30 
1251.3 
1.6292 


3-53 
1276.8 
I. 6561 


3-74 
1301.7 
1. 6810 


3-95 
1326.2 

I . 7043 


4.15 
1350.6 
1.7266 


170 . 

(368.5) 


Sp.V. 
A<2 
A^ 


2.68 
II95-4 
1.5590 


2.91 
1225.9 
1-5947 


3. 12 
1252.8 
1.6246 


3-34 
1278.4 
I. 6513 


3-54 
1303.3 
1.6762 


3.73 
1327.9 
1.6994 


3.92 
1352.3 
I. 7217 


180 

(373-1) 


Sp. V. 
AQ 
A0 


2.53 
1196.4 

I ■ 5543 


2.75 
1227.2 
I . 5904 


2.96 
1254.3 
I. 6201 


3-16 
1279.9 
1.6468 


3.35 
1304.8 
I. 6716 


3.54 
1329.5 
1.6948 


3-72 
1353-9 
I. 7169 


190 

(377.6) 


Sp.V. 
AQ 
A4> 


2.41 
1197.3 
1.5498 


2.62 
1228.6 
1.5862 


2.81 
1255-7 
I. 6159 


3-00 
1281.3 
1.6425 


3.19 
1306.3 
1.6627 


3-37 
1330.9 
I . 6904 


3-55 
1355.5 
I. 7124 


200 

(381.9) 


Sp.V. 
A(2 

A4> 


2^29 
1198.1 
1.5456 


2.49 
1229.8 
1.5823 


2.68 
1257.1 
1. 6120 


2.86 
1282.6 
1.6385 


304 
1307.7 
1.6632 


3.21 
1332.4 
1.6862 


3.38 
1357.0 
1.7082 


300 J 

(417. 5)| 


Sp. V. 
A(3 
A0 


1-55 
1204. I 
1.5129 


1 .69 
1240.3 
1.5530 


1.83 
1268.2 
I . 5824 


1.96 
1294.0 
1.6082 


2.09 
1319.3 
1.6323 


2.21 
1344.3 
1.6550 


2.33 
1369.2 
1.6765 


500 1 

(467.3)1 


Sp. V. 
A(3 
A0 


0.93 

1210.0 

1.470 


1.03 

1256 

1. 519 


1. 113 

1285 

1.548 


1.22 

1311 

1.573 


1.31 

1337 

1-597 


1.39 

1362 

1. 619 


1.47 

1388 

1.640 



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TEMPERATURE-ENTROPY DIAGRAM 

TO ACCOMPANY 

HEAT-POWER ENGINEERING 

C. F. HiRSHFELD AND Wm. N. BARNARD 

(Published by John Wiley & Sons) 
Redrawn (witi, permission) from larger diagram in Peabody's Steam and Entropy Tables (Wiley & Sons) 


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SYMBOLS. 

(The numbers refer to the pages where the symbol is first used in a new sense.) 



i^y 



A, area; ^,1 — ^ 1 ; A, 502; Apu, 107; ABEf, 537; a (area); ol, 328. 

B (Baume); Bd, BdK, Bi, Bik, 364; BCEf, 537; B.P., 562; B.t.u., i; b.h.p., 186. 

C, 257, 326; C,i4; Cp,35; a, 33; C£/, 188, 536; C£/c, 640; CEfh,Ho\ CF, 229; 

C.O.P., 735; c (const.). 

D, III, 579; DF, 325; d (differential coefficient); d, 130, 580; d.h.p., 186. 

E, 582; £/, 82; Efc, 164, 592, 641; Efh, 594, 641; Efn, 372, e (base for Naperian 

logs.); e.h.p., 186. 

F, 36, 57s; i^£, 562; FEf, 536; /, 575; f.h.p, 186. 

G, 662; G£/, 536; g (32.2 ft. sec). 

F, 338, 580; H.P., 234; A, 257, 578; h.p., 180; h.p.-hr., 180. 

/, 338; I.P., 234; lEf, 189; i.h.p., 184. 

-^,372. 

K, 335, 572, 639, 698; Kp, 35; Kv, 34; -^-E, 372; k (const.). 

L, 36, 184, 338, 575; L.P., 234; L.H.V., 488. 

Af, If', 502; MEf, 189; OT, 495; m.e.p., 184. 

n, 51, 184, 257, 643, 644, 646. 

OEf, 190; OEfd, OEfk, 363. 

■P, 33; Pm, 324; -Po, 698; ^, 325; pm, 184, 325; />,„//, pmL: pmR, 3331 ^^, 334- 

Q, 8; g, los; g/, ?/', 651. 

R, 32, 258, 315, 328, 372, 626; REf, 188; r, 49, 108, 258, 325; rff, r^, rr, 2,3^. 

S, 572, 626. 

T, 30; Ts, hi; r„ 105; r5£/, 537; rz?£/, 190; TDEf^, 365; r/£/, 190; 

T.U.E., 561; t, 30, 638; /a 499; ^c, ^d, 674; ^/, 499, 653; //, 653; ti, tm, 672; 

tv, 105. 
U.E., 561; u, 107, 133, 140, 371. 
V, 32, 286, 462; V, ss, 133; ^c, 680; Ves, 719; V„ 137; Fu,, 680; VEf, 720; 

D, 286, 371. 

W, 8, 14, 197, 258; Wc, 239; TFd, 191, 363; Wdj^, 363; PFj, 191; W/, W/K, 363; 

PFj, 239; w, 206, 372, 496, 653, 672; w', 654; Wc, 638; wf, 205; ze)/', 228; 

Wfo 205; Wh, 638; w//, 496; wn, 496. 
Z, 481; a;, HO, 479; Xf, Xk, 220. 
y, 108, 476, 481. 
■^, 647; 2, 575; 
a, 277, 625; 13, 627; 7, 38. 
A (finite change); A£, 11; AEp, AEs, 158; AEsx, 159; A/, AQ, 11; AQv, AQs, m; 

AQxp, 110; AQxs, hi; A^j/p, 109; AS, 11; A(/), 66; A^z), A0;, 119; A^s, 120; 

A<^sa, 120; A0!,., 119; A0X, 120. 

e, 259, 626; 9a, ^6, 639; dm, 572, 639. 
X, 108; p, 108; 0, 65; CO, 258. 



INDEX. 



156. 

vap.; 



196. 



Absolute temperature, 30. 

velocity, 371. 
Accumulator, 391. 
Adiabatic changes, of gas, 50-53. 

of sat. vapor, 153- 
of superheated 

157-159- 
in nozzles, 701. 
in steam engine, : 
reversible, 70. 
Admission, 275, 287. 
After burning, 409. 

Air, amt. for combustion, actual, 503-505. 
of C, 476-482. 
• of H, 486-487. 

deficiency of, 499. 

excess coefficient of, 480, 481, 498, 504. 
properties of, 477. 
Air card (int. comb, eng.), 406. 
Air compressor, clearance (effect of), 719. 
cooHng, 724. 
definitions, 716. 
efficiency, 722. 
elementary, 716. 
intercooling, 726. 
multistage, 726. 
real, 720. 

volumetric eflf. of, 722-724. 
work, 717, 718, 720. 
Air cyles, air engines, 730. 

compressors, 716-723. 
Air engines, 729. 
Air pumps, definition, 666. 
size of, 679. 
types, 677-678. 
Air required {see Air, amount). 
Air supply {see Air, amount). 
Air valve, auxiliary, 425. 
Alcohol, 469. 

engine performances, 451. 
Ammonia compressor, 745. 
refrigerator, 744. 
Analyses of coal, 457, 460-462, 509. 
natural gas, 470. 
producer gas, 602. 
Analysis of flue gas, 493-502. 
of coal, 460. 
proximate, 460. 
ultuimte, 460. 



Angle of advance, 277. 
nozzle, 373. 
range, 301. 
Angularity of rod, connecting, 272, 283-285. 

eccentric, 272, 284. 
Area {see Boiler, Condenser, Economizer, 
Feed Heater and Grate, Surface), 
chimney, 581, 583. 
indicator diagram (determination), 

184. 
meaning on PV-diagr., 47, 49, 74-79. 

on T</)-diagr., 74, 93, 138-140. 
negative, 46, 79. 
nozzles, 703, 705, 710. 
pipe, 711- 

piston, 184, H.P. and L.P., 328. 
piston rod allowance, 323. 
port opening, 286. 
positive, 46, 78. 
Ash, 459, 464, 510. 
A.S.M.E. Code, 209, 210, 535, 537. 
Associated heat, i, 9, 15. 
Atomizing, fuel oil, 530. 
Auxiliaries, power plant, 620, 653. 
Auxiliary air valve, 425. 

exhaust ports, 439. 
ports in valves, 289. 
Available hydrogen, 486. 

work of cycle, 79. 
Avogadro's law, 38, 478. 

Back pressure, steam eng., 214, 354. 

turbines, 367, 394. 
Back stroke, 271. 
Balance plate, 290, 291. 

piston (turbine), 389. 

ring, 292. 
Balanced valve, 291. 
Barometric tube (condenser), 666. 
Bernoulli's theorem (flow), 575. 
Bilgram diagram, 280. 
Blower, 716. 

producer, 614. 

turbo, 729. 

Blowing engine, 716, 729. 

Blow-ofI valve, 543, 560. 

Boiler {see Boiler types). 

accessibihty, 545. 

accessories, 560. 



795 



796 



INDEX 



Boiler capacity, 563- 

circulation, 542, 546. 
classification, 548. 
cleaning, 545, S47- 
compounds, 687, 688. 
counterflow, 541, SS8- 
corrugated flues, 550, 551. 
energy stream for, 534. 
efiSciencies, 537, 538, 540. 
explosions, 544. 

feed water, 547. (Sec Feed water.) 
header, 554. 
heat balance, 534. 
heat transmission, 540. 
heating surface, 538, 563, 564. 
horse power, 562. 
losses, S34. 

mud drum, 543, 554, 556. 
performance, 538, 561. 
plant, 692. 
power, 562. 
rating, 593. 
repairs, 546. 
safety of, 545. 
selection, 545. 
setting, 549, 551. 
size, 563. 
space, 547, sss. 
steam space, 547. 
suitability, 545. 
surface, 538-544. 

types, 548-560. {See Boiler types.) 
water legs, 555. 
Boiler types, 548-560. 

Babcock and Wilcox, 554. 

continental, 550. 

counterflow, 541, 558. 

double end, 559, 693. 

exposed tube, 549, 550. 

externally fired, 548, 551. 

fire tube, 548, 549. 

full front, 553. 

half front, 553. 

Heine, 555. 

horizontal, 548. 

horizontal return tubular, 552, 

internally fired, 548, 549. 

locomotive, 550. 

Niclausse, 559. 

Parker, 558. 

porcupine, 559. 

return tubular, 552, 553. 

Scotch marine, 551. 

sectional, 548, 554. 

Stirling, 556. 

submerged tube, 549, 550. 

tubular, 548, 549. 

tubulous, 548, 554. 

vertical, 548, 549. 

water tube, 548, 554. 



Boiler types, Wickes, 558. 
Boiling, 117. 
Boyle's law, 29 . 
Brake horse power, iSS. 
Breeching {see Flues) . 
British Thermal Unit, i, 6. 
B.t.u. per h.p.-hr., 180, 191. 
B.t.u. {see Calorific value) . 
Bucket losses, 370. 

velocity, 360. 
Buckets, turbine, 359. 
Burner, oil, 529-532. 

Calorific value, defined 492. 

Dulong's formula for, 462, 

463, 492. 
Mahler's curve for, 463. 
Calorific value of alcohol, 469. 
carbon, 475. 
carbon monoxide, 474. 
charcoal, 467. 
coal, 462-466. 
coke, 467. 
hydrogen, 486. 
hydrocarbons, 490-491. 
mixfures, 492. 
natural gas, 471. 
oils, 468-469. 
producer gas, 602. 
sulphur, 491. 
wood, 467. 
Calorimeters, steam, 224-227. 

fuel, 492, 493. 
Cam shaft, 406. 
Cams, 322, 440. 
Capacity, boiler, 562. 
furnace, 513. 
hot air engine, 398. 
ice making, 748. 
ice melting, 748. 
Carbon, combustion of, 472-486. 
fixed, 456, 459. 
volatile, 462. 
Carbon dioxide, formation, 474, 594. 
and furnace eff., 505. 
refrigeration, 745. 
Carbon monoxide, formation, 474, 594. 

method (of producer con- 
trol), 603. 
Carburetors, 423-425. 
Characteristic curve (governor), 264. 
Charcoal, 467. 
Charles' law, gas, 29-31. 

superheated vapor, 150. 
Chart, Mollier, 144, Appendix. 

r^, 137, Appendix. 
Chemical combination, heat from, 3-5. 

equilibrium (prod.), 594. 
Chimneys, area of, 581, 583. 
draft of , 579- 



INDEX 



797 



■Chimneys, height of, 580, 581, 583. 
Kent's formula for, 582. 
Kingsley's experiments on, 583. 
types of, 584-585. 
Circulating pump, 666. 

water (condenser), 672, 673. 
Circulation, boiler, 542, 546. 
convection, 629. 
Clapeyron's equation, 133. 
Clearance, definition, 203. 

effect on compression, 203. 
effect on cyl. condensation, 231. 
in air compressors, 719. 
in internal comb, eng., 404. 
measurement of, 323. 
radial (turbine), 386. 
Clinkers from coal, 511. 
CO2 recorders, 505. 
CO2 {see Carbon dioxide) . 
Coal, analysis of, 460-462, 509. 
anthracite, 457, 458, 465. 
"as received," 461. 
bituminous, 456-458, 465. 
briquets, 466, 514. 
caking, 465, 512, 598. 
calorific value of {see Cal. value). 
Carmel, 465. 
classification, 456. 
composition, 456, 459. 
Diederich's formula for, 462. 
"dry," 459. 

Dulong's formula for, 462. 
dust, use of, 466. 
fieldsof U. S., 458. 
firing of, 519, 520. 
formation of, 455. 
fuel value of, 462-466. 
geology of, 445. 
graphitic, 457. 
Mahler's curve for, 463. 
Marks' curve for, 461. 
moisture in, 464. 
noncaking, 465. 

rate of combustion of, 512, 513, 600, 
selection of, 515-517- 
semianthracite, 457, 458. 
semibituminous, 457, 458, 465. 
sizes of, 465, 466. 
soft, 456-458. 
sub-bituminous, 457. 
value as furnace fuel, 508-515. 
CoefiScient of contraction and discharge, 715. 
of excess air, 480, 481, 498, 504, 

SOS- 
of governor regulation, 257 . 
of performance (refrigeration), 
735, 739-741, 744, 747- 
■Coil, induction, 434. 
intensifier, 434. 
trembler, 437. 



Coke, 466-467. 

Coking arch, 524. 

Cold body, 80. 

Combined diagram, multiple-exp., 349. 

Combustible, 459, 472. 

Combustion, 472-502. 

actual, 503-532- 
air for, 476-482, 503-505. 
carbon, 472-486. 
complete, 472, 506-508. 
data, 473. 

hydrocarbons, 490-491. 
hydrogen, 486-490. 
line (int. comb, eng.), 411. 
mixtures, 491. 
oxygen for, 476. 
rate of, 508, 512-513, 600. 
recorders, 505. 
smokeless, 506-508. 
sulphur, 491. 
temperature of, 482-485. 
Combustion in furnaces, 503-532. 
air for, 503 . 

complete, 472, 506-508. 
rate of, 508, 512-513. 
smokeless, 506-508. 
Commercial considerations, 622. 

value of coal, 508-516. 
value of heating surface, 539. 
Composimeter, 505. 
Composition of {see Analyses of). 
Compoimds, boiler, 687, 688. 
Compressed air {see Air compressor). 
Compression, 44, 203. 

adiabatic, 50. 

constant pressure, 44. 

isothermal, 47. 

pressures in int. comb, eng., 

table of, 419. 
quality during, 214. 
steam engine, 275, 286, 288, 
293-295. 
Compressors, turbo, 729. {See Air comp.) 
Condensate, 20. 
Condensation, cylinder, 229. 
fraction, 229. 
initial, 212. 

reduction of, 123, 230-243. 
Condenser, advantages, 673. 
air in, 665. 

barometric tube, 666. 
electric (ignition), 437. 
essentials, 675. 
piping, 667, 677-680. 
pressures, 665. 
pumps, 666, 677. 
steam, 620, 664-677. 
surface of, 674. 
tail pipe, 665. 
types, 664-667. 



798 



INDEX 



Condensing, advisability of, 664. 
gains from, 235, 367. 
surface, 675. 
water, 20, 672-674. 
water recovery in, 681. 
Conduction, cyl. losses by, 214, 223. 

theory of, 624. 
Conductivity (heat), 625. 

specific (Table), 628. 
total, 635. 
Conjugate events, 275. 
Conservation of energy, 6. 
Constant entropy changes, gas, 70. 

vapors, 153-159. 
Constant heat curves (steam), 142. 
Constant pressure changes {see Isobaric 

changes.) 
Constant quality curves (steam), 140. 
Constant temperature changes {see Isother- 
mal changes). 
Constant volume changes {see Isovolumic 

changes.) 
Constant volume curves, steam, 140. 
Constants for flue gas, 479, 481 . 
ideal gas, 32. 
real gases, 38-41 . 
Consumption {see Performance). 
Contact resistance, 634. 
Continmty of state, 121. 
Convection (heat), 627. {See Boiler circ.) 
Conventional indicator diagram: 
for int. comb, engine, 406. 
for steam engine, 323-351. 
Cooling of condensing water, 681-684. 
of internal comb, eng., 407. 
of producers, 601 . 
of valves (int. comb, eng.), 439. 
ponds, 681. 
towers, 681-684. 
Cost, depreciation, 622. 
fixed charges, 623. 
operating, 623. 
St. Eng. vs. Turbine, 393. 
Counterflow, boiler, 541, 558. 
defined, 541. 

heat transmission, 641, 647. 
Cracking of oil, 427. 

in producers, 608. 
Crank end, 271. 
Critical conditions, 122. 
Critical pressure, gas, 122, 714. 

steam, 705. 
Critical temperature, gas, 122. 
Critical velocity gas, 714. 

steam, 705. 
Critical voliune, gas, 122. 
Crosshead, slotted, 272. 
Crude oil, 467-469. 
Culm, 466. 
Cushioning, 286. 



Cushion steam, 205. 
Cut-o£f, 275. 

changing in multi-exp. eng., 331, 

340-342- 
early, 288, 293, 295. 
governing int. comb, eng., 429. 
steam eng., 256, 352. 
influence on cyl. condensation, 232. 
in marine engines, 338. 
in simple engines, 233. 
in stationary engines, 337. 
limit of (Corliss), 312. 
range, 292. 
valve, 297, 300, 303. 
Cutting out of nozzles (turbine), 382. 
Cycle, available work of, 79. 

Beau de Rochas, 94-98. 
Bray ton, 98-100. 
Carnot, gas, 78-79. 

reversed, 84, 740. 
steam engine, 194. 
vapors, 161. 
Clausius, 167-173, 200-202. 
closed, 77. 
Diesel, 100. 
Ericsson, 93-94. 
four stroke, 403-414. 
gas, 76-102. 
Joule, 98-100. 
losses, 181. 
open, 77. 
Otto, 94-98. 

four stroke, 403-414. 
two stroke, 414-417. 
rectangular, 177. 
regenerative, gas, 90-93. 
steam, 199. 
Stirling, 90-93. 
two stroke, 414-417. . 
vapor, 161-179. 
Cylinder arrangement, 420-421. 

condensation, defined, 229. 

reduction, 230-243. 
efificiency, 188, 208, 370. 
feed, 205, indicated, 228. 
high pressure, 234. 
lagging, 240. 
losses, 23, 181. 
low pressure, 234. 
ratio, 334-340. 
surface in clearance, 231. 

Dalton's law, 116. 

and condensers, 665. 
Dash pot, 311. 

Deficiencies of air, losses from, 499. 
Degree of regulation, 257. 
Degree of superheat, in. 

determination of, 227. 
Delivered power, 185, 



INDEX 



799 



Delivered power, measurement of, 186. 
Density, specific, 
air, 477. 
gases, 40. 

steam, 134, Appendix. 
Deposits (scale), 686. 
Depreciation, 622. 
Diagram {see also Valve diagram). 

adiabatic changes of vapor on, 157. 

entropy, 119, Appendix. 

factor, 325-327, 3SI- 

of cycle, PV, 78. 

of energy stream {see Energy 

stream) . 
of gas curves, PV, 43, T<^, 73. 
of gas cycles, 89-102 . 
of heat flow {see Energj^ steam) . 
of producer plant, 25, 690. 
of steam plant, 18, 691. 
of T</) changes of vapors, 119. 
of vapor cycles, 162-179. 
of vaporization (heat changes), 

112. 
steam, 227. 
water rate, 227, 229. 
Diederich's equation (coal), 462. 
Diesel cycle, 100-102. 

efficiency, 447. 
engine, 417, 427- 
Displacement of valve, 273. 
Distillate, 468. 

Double deck boiler plant, 693. 
Draft, amount of, 578. 

apparatus, 574-589. 
artificial, 585. 
balanced, 587, 589, 615. 
chimney, 579. 
down, 522, 610. 
forced, 587, 588. 
friction head, 575, 576. 
furnace, 517-518. 
induced, 587, 589. 
mechanical, 587. 
natural, 579. 

pressure drop, 517, 574, 578, 581, 582. 
resistance, 574, 577. 
steam jet, 587, 588. 
Dry vacuum pump, 677. 
Diilong's formula, 462, 463, 492. 
Dutch oven, 522. 
Dynamics, of flow in nozzle, 371. 
of steam turbine, 371. 

Ebullition, 118. 
Eccentric, action of, 274. 

defined, 272. 

for int. comb, eng., 440. 

relative, 304. 

rod angularity, 272, 284. 
Econometer, 505. 



Economizer, boiler element, 559. 
fuel, 619, 660-663. 
producer, 6o5. 
surface, 662. 
Economy {see Performance). 
Effective power, 186. 
Efficiency, air compressor, 720. 

apparent (boiler), 537. 
boiler, 535-538. 
boiler and grate, 538. 
Brayton, 100. 
Carnot, gas, 82. 

general, 187. 
int. comb, eng., 445. 
steam engine, 194. 
vapors, 164, 165. 
Clausius, 170, 172. 
cold gas (producer), 593. 
combustion space (boiler), 536. 
CO2 and furnace, 505. 
cycle, 188. 

cylinder, 188, 208, 355, 370. 
Diesel, 102, 447. 
Ericsson, 94. 
furnace, 523, 536. 
grate, 523, 536. 
heat transmission, 639-649. 
hot air engine, 400-402. 
indicated, 188, 208, 355, 370. 
internal comb, eng., 445-447. 
mechanical, 189, 224, 413, 446. 
nozzle, 369, 708. 
Otto, 96, 410, 443-447. 
over-all, 190, 211. 
boiler, 538. 

internal comb, eng., 447. 
steam turbines, 363, 366, 
370. 
producer, 592-594. 
Rankine, 176, 177. 
rectangular PV, 178, 179. 
refrigeration {see Coef. of per- 
formance), 
regeneration, gas, 92. 

steam, 199. 
relative, 188, 445. 
shaft, 370. 
■ steam engine, 3SS-358. 
Stirling, 92. 
thermal, 190, 209, 210, 395, 443, 

446. 
thermodynamic {see Carnot). 
turbine, 365-370. 
volumetric, 411, 720-724. 
Electric energy (heat), 3. 
ignition, 434-438. 
Endothermic reaction, 472. 
Energy, associated heat, i, 9, 15. 

change of intrinsic, def., 11. 

of gases, 35. 



8oo 



INDEX 



Energy, change of intrinsic, of steam, 156- 
158. 
of vapors, 108. 
electric (lieat), 3. 
intrinsic, total, 4. 
kinetic (flow), 698-702, 708, 709. 
kinetic (molecular), 10. 
latent heat, 10-13. 
latent mechanical, 107 . 
potential, during vaporization, 13. 

(flow), 698, 699. 
radiant, 630. 
stream, boiler, 534. 

economizer, 660. 
feed water heater, 656, 657. 
general case, 187. 
internal comb, eng., 445. 
producer, 604. 
producer power plant, 25. 
steam power plant, 18. 
turbines, 369. 
Engine economies {see Performance). 
Engine {see Air engine. Blowing engine. 
Hot air engine. Internal combustion 
engine, and Steam engine) . 
Engine performance {see Performance). 
Engine room, 694. 
Entropy, absolute quantity of, 72. 
change, 68. 
constant, 70. 
of ideal gases, 67-72. 
of liquid, 119. 
of steam, 132. 
of superheating, 119. 
of superheated vapor, 1 20. 
of vaporization, 119. 
total, of steam, 137, Appendix. 
Equalizing pipe (turbine), 389 
Equilibrium, chemical, 594. 
Equilateral hyperbola, 54, 324. 
Equivalent, evaporation, 561. 

molecular weight, 495. 
Ericsson cycle, 93-94- 

hot-air engine, 397-401. 
Ether vapor, T<^-diagram, 154. 
Evaporating pan, 620, 649. 
Evaporation, definition, 115. 
equivalent, 561. 
factor of, 562. 
rates (boiler), 563. 
unit, 561. 
Events, valve, 274, 275. 
Excess air (combustion), 478-481, 504, 505. 
coefiicient, 480, 481, 498, 504. 
percentage, 497. 
Exhaust lap, 273. 

lap circle, 282. 

lap line, 276. 

losses, int. comb, eng., 448. 

pipe area, 711. 

ports, auxiliary, 439. 



Exhaust valves, int. comb, eng., 439. 

valve timing, 441. 
Exhaust steam, in contact with walls, 232. 

turbine, 367, 390, 396. 
Exhauster, induced draft, 588. 

producer, 614. 
Exothermic reaction, 472. 
Expansion, adiabatic, gas, 50-53. 

in nozzles, 701. 
in steam engines, 196. 
vapors, 153-159. 
constant pressure {see Expan- 
sion, isobaric). 
constant temperature {see Ex- 
pansion, isothermal), 
constant volume {see Expansion, 

isovolumic). 
definition, 44. 
free, 63-64. 

general curves of, 54, 55. 
incomplete, 213, 732. 
in steam engines, 195, 196. 
isobaric, of gas, 44. 

vapors, 146. 
isothermal, of gas, 47. 

vapors, 146. 
isovolumic, of gas, 46. 

vapors, 159, 160. 
line (real int. comb, eng.), 412. 
piping (of), 696. 
ratio, 48, 330-340. 
valve (refrigerator), 743. 
Explosions, boiler, 544. 

producer, 614. 
External combustion engine, 397-402. - 
latent heat, 10, 13, 107. 
work, 10, 13, 107. 
valve, 273. 
Extractor, tar, 616. 

Factor of evaporation, 562. 

Fan (draft), 588. 

Feed water heaters, 651-663 . 

advantages, 651, 655. 

economizer, 660-663. 

heating surface, 659. 

heat saving, 651. 

horse power, 659. 

saving, 651, 655. 

size, 659. 

surface (extent), 659. 

temperature increase, 653 . 

types, 654-658. 

water saved, 654. 
Feed water impurities and treatment, 685. 
Figure of merit {see Coef. of performance). 
Financial considerations, 622. 
Firing of coal, hand, 519. 

stoker, 520. 
First law of thermodjmamics, 6. 
Fixed carbon, 456, 459. 



INDEX 



80 1 



Fixed charges, 623. 
Flame length, 507, 522. 
Flexible shaft (turbine), 376. 
Floor space, boiler, 547, 555. 

engine vs. turbine, 392. 
Flow, Bernoulli's theorem, 575. 
counter (theory), 641, 647. 
gas and vapor, 698-715. 
Grashof s formula, 710. 
ideal gas, 712. 
imperfect gas, 715. 
Napier's formula, 710. 
parallel, 640, 644. 
pipes (in), 710. 
saturated steam, 700. 
unidirectional (engine), 242. 
velocity of gas, 713. 

of steam, 703. 
Flue gas analysis, 477-482, 493-502. 

loss {see Stack losses). 
Flues, 574- 

Fluid friction loss, int. comb, eng., 413. 
Fluttering of valve (air), 721. 
Foaming, 685, 687. 
Foot pound (unit), 180. 
Forward stroke, 271. 
Free expansion, 63-64. 
Friction, fluid (in int. comb, eng.), 413. 
head (flue gas), 575. 
horse power, 186. 
losses, 181. 

mechanism, int. comb, eng., 413. 
steam engine, 358. 
steam turbine, 370. 
valve, 291. 
Fuels, alcohol, 469. 

artificial gas, 471. 
charcoal, 467. 
coal, 455-467. 
coke, 466-467. 

consumption of {see Performance), 
culm, 466. 
definition of, 455. 
fuel oil, 468. 
gasohne, 468. 
graphitic coal, 457-458. 
industrial wastes, 467. 
kerosene, 468. 
lignite, 456-458, 465. 
municipal waste, 467. 
naphtha, 468. 
natural gas, 470. 
oil, 467-469. 
peat, 456, 464. 
petroleum, 467-469. 
prepared, 455. 
producer gas, 471, 590, 602. 
wood, 467. 
Fuel calorimeter, 492. 
Fuel oil, 468. 



Fuel oil, atomizing, 530. 

burning, 529-532. 
Fuel values {see Calorific values). 
Full peripheral discharge, 385. 
Furnace efficiency, 505. 

capacity, 513. 

fittings, 521. 

grates, 520. 

length, 522. 

losses, 533. 

oil burning, 529. 

operation, 517-520. 

rate of combustion in, 513. 

size for coal, 513. 
for oil, 530. 

stokers (automatic), 523-529. 

types, 521-523. 

volume, 507. 
Fusible plugs, 560. 

Gain from decreasing back pressure: 
in steam engine, 235. 
in steam turbine, 367, 394. 
Gain from superheating: 
in steam engine, 236, 354. 
in steam turbine, 367, 394. 
Gamma, 38. 

value of, 41 . 
Gas analyses {see Analysis). 

analyses (flue), 477-483, 493-502. 
artificial, 471. 
constants, ideal, 32. 

real, 38-41. 
cycles, 76-102. 
defined, 28, 123. 
expansions, 43-58. 
from oil, 617. 
ideal, 29. 
laws, 28-42. 
natural, 470. 
producer, 471, 590, 602. 
specific densities of, 40. 
specific heats of, 33-38. 
specific volumes of, 41. 
Gas engines {see External combustion en- 
gine, Internal combustion engine, and 
Performance) . 
Gas producer, apparatus (general), 590. 

carbon monoxide method, 

603. 
coohng, 601-607. 
cleaning apparatus, 615. 
efficiency, 592. 
fuels for, 607. 
hydrocarbons, effect of, 

607. 
Hmitations, 598. 
mechanical charging, 615. 
oil, 617. 
size, 600. 



802 



INDEX 



Gas producer, temperature control, 603, 
theory, advanced, 594- 

simple, 590. 
types, 608-615. 

balanced draft, 615. 
double zone, 610. 
downdraft, 609-610. 
grate bottom, 612. 
pressure, 613. 
suction, 614. 
updraft, 608. 
water bottom, 612. 
Gaseous state, region of, 123. 
Gasoline, 468. {See Performance.) 
Gauge pressure, 182. 
Gay Lussac's law, 29. 
Gears, turbine, 376. 

valve {see Valve gear). 
Governing, constant speed, 255. 
cut-off, 256. 
internal combustion engine, 

427-431,441-442. 
isochronous, 260-261. 
methods, 255. 
quahty, 429. 
quantity, 429. 
resistance, 255. 
stable, 263. 
steam engines, 256. 
throttling, 256, 342, 352, 429- 
turbines, 376, 382, 389. 
unstable, 260. 
Governors, 255-270. 

adjustment of, 264, 270. 
Armstrong, 269. 
centrifugal, 266. 
characteristics of, 264. 
conical, 257. 
fiyball, 257-262. 
inertia, 267. 
isochronous, 260, 261. 
loaded, 257. 
pendulum, 257-262. 
Porter, 259. 
Rites, 267. 
shaft, 262-270. 
speed limitations of, 258. 
speed variation of, 256. 
Sweet, 266. 
theory, fiyball type, 257. 

shaft type, 262. 
Watt, 257. 
weighted, 259. 
Grain alcohol, 469. 
Graphitic coal, 457-458. 
Grashof's formula, 710. 
Grates, area of, 518. 

boiler, 520-523. 
efficiency of, 536. 
producer, 612. 



Half time shaft, 406. 
Hammering (of engine), 287. 
Head end, 271. 
Header (boiler), 554. 
Heat, associated, i, 15, 19. 
balance, boiler, 534. 

int. comb, engine, 447-449. 
steam engiae (Hirn's), 219. 
changes of intrinsic, definition, 11. 
gases, 35. 
steam, 156, 158. 
vapors, 108. 
latent, 10, 13, 106-108. 
specific {see Specific heat) . 
total, steam, 130, 137. 
vapor, 108. 
Heat changes during: 
isobaric changes of gases, 45 . 

vapors, 147, 149. 
isothermal changes of gases, 49. 

vapors, 152. 
isovolumic changes of gases, 46. 

vapors, 159, 160. 
Heat conduction (theory), 624. 
Heat conductivity, 625. 
Heat consumption {see Performance). 
Heat flow diagram {see Energy stream). 
Heat from chemical combination, 3-5. 
electrical energy, 3. 
mechanical energy, 3. 
sun, 2. 
Heat interchange with cylinder, 214-217. 
Heat of, combustion, 492. 
liquid, 105, 129. 

area for, 138. 
meaning of term, 108. 
steam, 130. 

area for, 139. 
superheat, iii, 136, 137. 
vapor, total, 108. 
vaporization, latent, 106, 108. 
Heat resistance, 626. 
Heat transmission, actual, 632. 

boiler, 538, 540-544. 
cases of, 639-650. 
condenser, 675. 
conduction, 624. 
convection, 627. 
economizer, 662. 
feed water heater, 659. 
heating surface, 636. 
radiation, 632. 
superheater, 572. 
{See Rate.) 
Heat unit, i, 6, 561. 
Heat utilization, evaporating pans, 620. 
heating, 621. 
industrial processes, 620. 
Heat value, calorimeters, 492. 

higher, 462, 487-490, 492. 



INDEX 



803 



Heat value, lower, 462, 487-490, 492. 
Heat value {see Calorific value) . 
Heater {see Feed water heaters, Econo- 
mizers) . 
Heating surface, boiler, 538, 563. 

commercial value of, 539. 

economizer, 662. 

effective, 636. 

extent, 639. 

feed heater, 659. 

mean temperature, 637- 

639- 
superheater, 572. 
Heavy oils in internal comb, eng., 426-427. 
Height of chimney, 581-583. 
High pressure cylinder, 234. 
High pressure, effect on cylinder condensa- 
tion, 241, 354. 
on turbines, 394. 
Higher heat value, 462, 487-490, 492. 
Hirn's analyses, 219-223, 235. 
Horse power, boiler, 582. 
brake, 186. 
defined, 180. 
delivered, 186. 
effective, 186. 
friction, 186. 

heat equivalent, 180, 191. 
heater, 659. 
indicated, 183, 184. 
Hot air engine, 397-402. 
Hot body, 80. 

Hot bulb (head) engine, 426. 
Hot gas efficiency (product), 594. 
Hot well, 20. 

Humidity, effect on stack losses, 502. 
Hydraulic inches, 575. 
Hydrocarbons, 490-491. 
Hydrogen, available, 486. 

combustion of, 486-490. 
higher heat value of, 487. 
lower heat value of, 487. 
Hyperbola, equilateral, 54, 324. 

Ice machine {see Refrigeration). 
Ice making capacity, 748. 
Ice melting capacity, 748. 
Ideal gas, 29. 

mechanism, 7. 

vs. real engine, 180. 
Ignition, internal comb, engine, 433-438. 
Impurities (feed water), 685. 
Incomplete combustion in furnace, 472, 481, 
501. 
losses in gas engine, 448. 
Incomplete expansion, 213, 732. 
Incrustation, 686. 
Indicator, 181. 
Indicator diagram, area of, 184. 

conventional, 323-351, 406. 



Indicator diagram, four-stroke cycle, 406- 
412. 
meaning of, 182. 
multiple-exp. eng., 349. 
scales, 182-187. 
two-stroke cycle, 415-417. 
Indicated cylinder efficiency, 188, 208, 446. 
cylinder feed, 228. 
horse power, 183, 184. 
steam consumption, 227. 
work, 183, 413. 
Induction coil, 434. 
Initial condensation (definition), 212. 
Injection water (condenser), 672, 673. 
Injectors, 712. 
Inlet valve, internal comb, engine, 439. 

timing, 441. 
Insulating film (gas), 635. 
Intensifier coil, 434. 
Intercooling (air compressor), 726. 
Interest, 623. 

Interchange heat in engine cyl., 214-217. 
Internal combustion engine: 

actual, 403-454. 

advantages and types of, 403. 

after burning, 409. 

air card, 406. 

cam shaft, 406. 

cams, 440. 

classification of, 421-423. 

clearance space, 404. 

combustion in, 412. 

combustion line, 411. 

compression pressures, 418. 

cooling, 407. 

cylinder arrangements, 420. 

definition of, 397. 

diagrams (indicator), 406-412, 

Diesel, 417, 427, 447. 

double-acting, 420. 

eccentrics, 440. 

efficiency, 412, 443-454. 

four-stroke cycle, 403-414. 

fuel consumption of {see Performance). 

fuels, 418. 

fuels, modification for, 418. 

governing, 427-431. 

guarantees, 450-454. 

heat balance, 447. 

heavy oil in, 426, 427. 

hot bulb (head), 426. 

ignition methods, 433-438. 

indicator diagrams, 406-413. 

indicated work, 413. 

Koerting, 416. 

losses in, 410, 447-449. 

mechanical efficiency of, 413. 

mechanical features of, 420-442. 

oil engine, 454. 

Otto efficiency, 413. 



8o4 



INDEX 



Internal combustion engine: 
Otto type, 403. 

performance {see Performance), 
power per cylinder, 420. 
scavenging, 412. 
size of, 420. 

single- and double-acting, 420. 
suction line, 409. 
tandem, 422. 
turning effort of, 420. 
twin, 422. 

two-strolce cycle, 403, 414-417. 
valve gears, 438-442. 
vertical vs. horizontal, 421. 
working substance of, 403. 
Internal latent heat, 10-13, 108. 
Internal valve, 273. 
Intrinsic energy, 4, 11, 35. 

change of, 11. 
Intrinsic heat change, 11. 

gases, 35. 
steam, 156-158. 
vapors, 108. 
Irreversible process, 59-64. 
Isentropic changes of gases, 70. 

vapors, 153-159- 
Isentropics, 70. 

Isobaric changes of gases, 44-45- 
steam, 142. 
vapors, 146-149. 
Isochronous governing, 260-261. 
Isothermal changes of gases, 44-49. 

vapors, 146-151. 
Isothermalcompression (steam engine), 19! 
Isothermal expansion (steam engine), 196. 
Isovolumic changes of gas, 44-47- 
steam, 140. 
vapors, 1 59-161. 

Jacket losses, 447. 

Jackets, air compressor, 725. 

internal combustion engine, 407. 

steam engine, 238-240. 
Joule's experiment, 63. 
Junction box (boiler), 559. 

Kent's formula (chimney), 582. 
Kerosene, 468. 

Kingsley's experiments (chimneys), 583. 
Kinetic energy of flow, general, 698, 700. 
steam, 702. 

Labyrinth passage, 387- 
Lagged cylinders, 240. 
Lap, 273, 280, 276, 282. 
Latent heat, 106-108. 

energy, 10, 13. 

internal, 10, 13. 
Latent heat of vaporization, external, 107. 
internal, 108. 



Latent heat of vaporization, total, 108. 
Latent mechanical energy, 107. 
Law, Avogadro's, 38. 
Boyle's, 29. 
Charles', gas, 29, 31. 

superheated vapor, 150. 
conservation of energy, 6. 
Dalton's, 116. 
gases, 28-33. 
Gay Lussac's, 29. 
Marriotte's, 29. 
partial pressures, 117. 
Stefan's, 630. 
thermodynamics, first, 6. 

second, 8. 
Willans', 352. 
Lead (valve), 276. 
Leakage, steam engine, 214, 230. 

turbines, 369. 
Lignite, 456-458, 465. 
Limitations of simple valve, 288. 

producers, 598. 
Line of transference, 329. 
Liquid and gaseous states (continuity of), 

121. 
Liquid, ebullition, 118. 
entropy, 119. 
heat of, 105, 129. 
pressure within, 117. 
region of, 123. 
specific volume of, 113. 
Liquid fuel, burning, 529-532. 
Load, distribution of (compoimd eng.), 
338-341. 
effect on water rate, 233. 
factor, 354. 

range of (high-speed engine), 292. 
Logarithm, tables, Appendix, 
use of. Appendix. 
Logarithmic cross-section paper, 55. 
Loops (combined diagrams), 342, 413. 
Losses, boiler, 534. 
bucket, 370. 

chimney (see Losses, stack), 
cycle, 181. 

cylinder, 23, 181, 214, 223. 
flue gas, 498. 
friction, 181. 
furnace, 533-536. 
grate, 533-536. 

int. comb, eng., 410, 413, 447-449. 
jacket (int. comb, eng.), 447. 
mechanical, 181. 
nozzle, 369, 708. 
producer, 592-594, 604, 606. 
radiation, 447. 
stack, 498-502. 
steam engine, 194. 
turbine, 369-370. 
impreventable (boiler), 534. 



INDEX 



805 



Low-pressure cylinder, 234. 
Low-pressure turbine, 390, 396. 
Lower heat value, 462, 487-492. 

MacFarlane-Graj''s formula, 315. 
Mahler's curve (coal), 463. 
Marine propulsion by turbines, 391. 
Marks' curve (coal), 461. 
Marriotte's law, 29. 

Maximum thrust (compound engine), 332. 
Maximum valve opening, 286, 295. 
Mean effective pressure, 184. 

referred, 328. 
Mean hydraulic radius, 576. 
Mean specific heats of gas, 484-485. 

of superheated steam, 136. 
Mean temperature head, heat transmission, 

Cases I-IV, 639-649. 
Mechanical energy, heat from, 3. 

latent, 107. 
Method of ordinates (area), 185. 
Mixture of elements (combustion of), 491- 

492. 
Moisture in coal, 459, 464, 509. 

loss in flue gas, 502. 
Mollier chart, 144, Appendix. 
Motion, perpetual, ist type, 7, 88. 

2d type, 7, 9, 87, 88. 
3d type, 7, 8s, 88. 
Mud drum, 543, 555, 556. 
Multipass, boiler, 554. 

condenser, 673. 
Multiple effect, 650. 
Multiple-expansion engine, 234. 
changing cut-off in, 340-342. 
combined diagrams, 349. 
conventional diagrams, 327. 
cylinder ratios, 336-340. 
distribution of work, 338. 
expansion ratios, 336-340. 
indicator diagram, 340. 
PV-diagram, 348. 
Mimicipal waste (fuel), 467. 

n, SI, 184, 2S7- 

n, value for air compressors, 721, 725. 
gas adiabatics, 52. 
steam adiabatics, 156. 
Napier's formula (flow), 710. 
Naphtha, 468. 
Natural fuels, 455. 
gas, 470. 
oil, 467r469. 
Neck of nozzle, 704, 714. 

Grashof's rule, 710. 
Napier's rule, 710. 
Negative work, area, 46. 

definition, 79. 
Network, 79. 
Noncaking coal, 465, 



Nonconducting materia's, 240, 241. 
Normal power, 353. 
Nozzle, applications, 712. 

area, 703. 

gas, 7I2-7IS- 

Grashof's formula, 710. 

loss, 369, 708. 

Napier's formula, 710. 

neck, 704, 714. 

steam, 703, 709. 

Oil, burning of, S29-S32. 
distillates, 467. 
feeding systems, 250. 
kinds, 467. 
petroleum, 467. 
producer gas from, 617. 
Opening, diagram, 278. 
early, 287. 
valve, 273. 
Operating costs, 623. 
Overload capacity of boiler, 563. 
Overload, effect on water rate, 233. 

valve, 366, 389, 394- 
Oxygen for combustion, 476-482. 

Parallel flow, 640, 644. 
Parr's classification, 458. 
Partial pressures, 117. 

in condensers, 665. 
Passes, boiler, SS4- 

condenser, 673. 
Peat, 456, 464. 
Performance, boiler, S38, 561. 

coefiicient of, 73S-736, 739, 

741, 744, 747. 
comparison of (true), 191,354. 
defined, 191. 
heat basis, 191. 
ice machines {see Refrigera- 
tion) . 
int. comb.eng., 449-454. 
refrigeration, 735-736, 739. 

741, 744, 747. 
steam engine, 223, 352-358. 
steam turbine, 393-396. 
Periods of valve operation, 274. 
Perpetual motion, ist tj'pe, 7, 88. 

2d type, 7, 9, 87, 88. 
3d type, 7, 85, 88. 
Petroleum, 467-469. 

burning, 529. 
Pipes, steam flow in, 710. 
Piping, boiler, 697. 

condenser, 667, 677. 
expansion of, 696. 
feed water heater, 659. 
power plants, 694. 
steam, 694. 
Piston, balance (turbine), 389. 



8o6 



INDEX 



Piston speed, 245, 246. 
Pitch in producer, 607. 
Planimeter, 184. 
Plant {see Power plant). 
Pond, cooling, 681. 
Port, areas, 285. 

auxiliary, in valves, 289. 
auxiliary exhaust, 439. 
openings, 285. 
Positive work area, 46. 

definition, 78. 
Potential energy (flow), 698, 699. 

of vaporization {see Latent heat). 
Potential heat, 537. 
Power, 180. 

air refrigeration, 739. 
boiler, 562. 
brake, 186. 
delivered, 186. 
effective, 186. 

external comb, eng., 397, 399. 
friction, 186. 
horse, 180. 
indicated, 184. 

internal comb, eng., 413, 414. 
normal, 353. 
per cycle, 420. 
producer gas, 24. 
rated, 353. 
Power plant, 16, 24, 690-697. 
choice, 690. 

heat flow diagram, 18, 25. 
internal comb, eng., 25, 690. 
piping {see Piping), 
steam, 16, 690-697. 
Preheater, compressed air engine, 732. 

producer, 606. 
Preignition, 412, 418. 
Prepared fuels, 455. 
Pressure, back, steam engine, 214. 
turbine, 367. 
compression, int. comb, eng., 418, 

419. 
constant {see Isobaric). 
critical, gas, 714. 

steam, 705. 
drop in flue, 574, 578. 
effect on economy, 241, 354, 394. 
gauge, 182. 
heating system, 621. 
mean effective, 184. 
m.e.p., 184. 
of mixture, 117. 
referred m.e.p., 328. 
stages (turbine), 381. 
usual steam, 241. 
within a liquid, 117. 
Pressure-volume diagram (area), 47, 74, 79. 
Price of coal, basis of, 509. 
Prime mover, 16. 



Process, irreversible, 59-64. 

reversible, 59. 
Producer gas, 590-618. 

analyses, 602. 
oil, 617. 
plant, 24. 
Producers (see Gas producers). 
Progressive distillation of vol. matter, 525. 

oil, 468. 
Progressive specific heat (steam), 130. 
Properties of air, 477. 

gases {see Gas constants), 
steam, 126-145, Appendix, 
sources, 127. 
Propulsion by turbine, 391. 
Proximate analysis of coal, 460-462. 
Pumps, air, 667, 677-680. 
circulating, 666. 
dry vacuum, 677. 
feed, 697. 
tail, 667, 669. 
vacuum, 666, 677-680. 
wet vacuum, 678. 
PV-quantity, 345-347- 



q, 105. 

Q, 8. 

Quadruple expansion engine, 234, 339. 

Quality, no. 

curves, 139, 154, 206, 351. 

during compression, 214. 

factor, no. 
Quality governing, 429. 
Quantity governing, 429. 
Quintuple expansion engine, 234. 



r, 49. 131, 334- 

R, 32, 38, 40, 41, 334. 

Racing, 427. 

Radial clearance (turbine), 386. 

Radiant energy, 630. 

Radiation (heat), 629. 

losses, in int. comb, engine, 447. 
in steam engine, 214, 223. 
in turbine, 370. 
misuse of term, 632. 
Range, angle, 301. 

of cut-off, 292. 
Rate of combustion of coal, 512-513. 
combustion and smoke, 508. 
consumption of working substance, 

191- 
fuel consumption, 191. 
See Performance, Heat Trans- 
mission. 
Rated power, 353. 

boiler, 563. 
Rating of boiler, 563. 

refrigeration mach., 748. 



INDEX 



807 



Ratio of expansion, 48. 

in multiple exp. eng., 334, 340. 
in simple eng., 234. 
Reaction, endothermic, 472. 
exothermic, 472. 
reversing, 476. 
Real and ideal engines, 180. 
Receiver, air, 732. 

infinite, 330. 
line, 329. 
reheating, 240. 
steam engine, 240, 251. 
Receiver pressure, formula for, 335. 
selection of, 331. 
with no clearance, 332. 
Reciprocating parts, 244. 

cushioning of, 286. 
Rectangular PV-diagram, 177-179. 
Referred m.e.p., 328. 
Refrigeration, air machine, 738. 

absorption process, 746. 

ammonia, 746. 

coefficient of performance, 

735, 739. 741, 744, 747- 
materials for, 744. 
mechanical, 734. 
rating, 748. 

thermodynamics of, 734. 
vapor compr. machine, 741. 
vapors, kinds, 744. - 
Regenerator, 90. 

turbine, 391. 
Region of gaseous and Uquid state, 123. 
saturation, 114. 
superheat, 1 14-123. 
Regulation coefficient, 257. 
Reheating receiver, 240. 
Relative eccentric, 304. 
velocity, 371. 
Release, 275. 

early, 288, 293, 295, 347. 
Resistance, contact, 634. 

governing, 255. 
heat, 626. 
surface, 634. 
Resistance to iiow (flue gas), 574. 
Reversed Carnot cycle, 84. 

refrigeration, 740. 
Reversed chemical reaction, 476. 
Reversible adiabatics, 70. 
isentropics, 70. 
processes, 59. 
Reversibility, 59-64. 
Revolutions per minute, 246. 

effect on cyl. cond., 241. 
Rider hot-air engine, 398, 400. 
Ripper's experiment (sup. steam), 237. 
Rites' inertia governor, 267. 
Rotary air pump, 678. 
engines, 248. 



Rotating parts of st. eng., 244. 
Rotative speed, efiect on cyl. cond., 241. 

of Corliss engines, 246. 
Rotor, 359. 
Running over and under, 250. 

Safety cam, 313. 

valve, 560. 
Saturated steam, properties, 126-135, 

Appendix. 
Saturated vapors, 109, iii. 

defining condition of, 115. 
properties of, 103-110. 
Saturation curve, 113. 

for mult. exp. eng., 351. 
steam, 139, 206. 
Scale, boiler, 686. 

of indicator diagram, 182-183. 
Scavenging engine, 412. 
Scotch yoke, 272. 
Scrubber, dry, wet, 616. 
Second law of thermodynamics, 8, 9. 
Sensible heat, 11. 

change of, 36. 
flue gas, 501. 
producer gas, 593, 601. 
Sentinel whistle, 560. 
Separator, steam, 697. 
Shaft for high-speed turbine, 376. 

half time, 406. 
Shroud ring, 376. 
Simple engine vs. compound, 233. 
Single effect vacuum pan, 649. 
Sleeve motors, 438. 
Slide valve {see Valves). 
Slotted crosshead, 272. 
Smoke, composition of, 508. 

prevention of, 506-508. 
Soft coal, 456-458. 
Solar heat, 2. 
Spark plug, 436. 
Specific density of gases, 38-41. 

steam, 134, Appendix. 
Specific heat, 14. 

conductivity, 625, 628. 
gases, 484-485. 
ideal gas, 33-35- 
mean, 14. 
progressive, 130. 
steam, 130. 
superheat, 135-136. 
true, 15-34- 
variable, 15. 
Specific volume of gases, 38-41. 

steam, 133, Appendix, 
super, steam, 137. 
vapors, 113. 
Speed, piston, 245, 246, 286. 

rotative, efiect on cyl. cond., 241. 

of low-speed engines, 246. 



8o8 



INDEX 



Spontaneous ignition, 418, 434. 
Stack {see Chimney), losses, 498-502. 
Stagnant film, 635. 
State, continuity of, 121. 
Steam data, 127. 

properties of, 126-145, Appendix, 
saturated (table). Appendix, 
specific heat of, 130-136. 
superheated, 135-137, Appendix. 
Steam, behavior of, in cyUnder, 208-229. 
Steam calorimeter, 224-227. 
Steam consumption {see Performance). 
Steam distribution chart, 344. 
Steam engine {see Steam engine types) : 
action of steam in, 208-229. 
Carnot cycle and, 194. 
classification of, 245-254. 
compared with turbine, 360. 
comp. and exp. lines, 195-196. 
consumption, 197-202, 352-358. 
cycles, 161-179, 194-207. 
cylinder condensation, 230-243. 
diagrams (indicator), 323-351. 
efficiencies, 186-191. 
data, 356-358. 
governors, 255-270. 
jackets, 238-240. 
losses, 194. 
parts, 244. 
performance, 353-358. 

data, 354-358. 
determination, 223. 
steam consmnption, actual, 205, 352-358. 

indicated, 227. 
theoretical, 194-207. 

types, 245-254 {see Steam engine types), 
valves and gears, 271-322. 
water rate, actual curves, 232. 
data, 354-358. 
defined, 224. 
diagram, 229. 
Steam engine types: 

angle compound, 252. 

center crank, 250. 

compound, 233, 234. 

Corliss, 247. 

cross compound, 251. 

double acting, 248. 

duplex compound, 252. 

high speed, 245, 292, 293, 308. 

inclosed, 250. 

lokomobile, 240. 

left hand, 249. 

low speed, 246. 

marine, 253, 338. 

medium speed, 246. 

multiple expansion, 335. 

oscillating, 249. 

quadruple expansion, 234, 339. 

quintuple expansion, 234. 



Steam engine types: 

reciprocating, 248. 
reversing, 254. 
right hand, 249. 
self oiling, 250. 
' side crank, 249. 
single acting, 248. 
steeple compound, 251. 
straight flow, 242. 
tandem, 250. 

triple expansion, 234, 336, 338. 
unidirectional flow, 242. 
Woolf, 328. 
Steam heating, 621. 
Steam injector, 712. 
Steam jacketing, 238-240. 
Steam jets, 587, 588. 

blowers (producer), 613. 
Steam nozzle {see Nozzle), 703. 
Steam pipes {see Pipes), 711. 

piping, 694. 
Steam power plants, 16, 690-697. 
Steam properties {see Steam). 
Steam turbine, 359-396. 

accumulator, 391. 

advantages, 392. 

Alhs-Chahners, 389. 

applications, 390. 

back pressure (effect), 367, 

BUss, 384. 

Branca's, 359. 

classification. 

clearance, 386. 

Curtis, 375> 380. 

defined, 359. 

De Laval, 373. 

dynamics, 371. 

double flow, 386. 

efficiency, 363-365- 

Electra, 382. 

energy stream, 369. 

exhaust steam, 367, 390, 396. 

flexible shaft, 376. 

gears, 376. 

governing, 368, 382, 389. 

heat supplied, 364. 

Hero's, 359. 

impulse, 359, 360. 

Kerr, 379. 

labyrinth, 387. 

leakage, 367. 

losses, 369-370. 

low pressure, 367, 390, 396. 

marine propulsion, 391. 

multi-stage, 361, 379, 390. 

nozzle, 359-361. 

losses, 369. 
theory, 697-715. 
overload, capacity, 366. 
valve, 366, 394. 



INDEX 



Steaxa turbine, Pelton, 379. 

performance of {see Performance). 
Parsons, 375. 387- 
pilot valve, 382. 
pressure stage, 381. 
Rateau, 374, 379, 394. 
reaction, 360, 384, 387. 
Riedler-Stumpf, 383. 
rotor, 359. 
shroud ring, 376. 
single-stage, 379. 
small vs. large, 395. 
Sturtevant, 384. 
superheated steam with, 367. 
Terry, 383. 
tests, 395- 

thermodynamics of, 362, 369. 
velocity compounding, 380, 382. 
water rate, 363, 365. 
water seal, 379. 
Westinghouse-Parsons, 389. 
windage, 365. 
Zoelly, 374, 380. 
Stefan's law (radiation), 630. 
Stokers, 520, 523-529. 
Stoking {see Firing). 
Stratification, furnace gases, 507 
Stroke, back, 271. 

forward, 271. 
Suction line, 409. 

producer, 614. 
Sulphur, combustion of, 491. 

dioxide refrigeration, 745. 
in coal, 464, 511. 
Superheat, degree of, iii. 

determination of, 227. 
Superheated steam {see Steam), effect on, 
cylinder cond., 236-238, 354. 
steam turbine, 367, 394. 
Superheated vapor, in. 

Charles' law for, 150. 
properties of, 111-115. 
region, 123. 
Superheater, 127, 565-573. 

advantages, 236-238, 367, 565. 
arrangements, 567. 
protection of, 571. 
surface, 572. 
types, 566. 
Surface, boiler, 538, 563. 
condenser, 675. 
economizer, 662. 
effect of clearance, 231. 
feed water heater, 659. 
resistance, 634. 
superheater, 572. 
water in boiler, 546. 

t, 30, 
T,30. 



T<^-diagram, chart. Appendix. 

derived from PV, 217, 218. 
Table I, 40; II, 58; III, 102; IV, 241; V, 325; 
VI, 32s; VII, 35S; VIII, 358; IX, 358; 

X, 39s; XI, 419; XII, 443; XIII, 457; 

XIV, 458; XV, 460; XVI, 46s; XVII, 
466; XVIII, 470; XIX, 473; XX, 477; 
XXI, 479; XXII, 481; XXIII, 491; 
XXIV, 578; XXV, 602; XXVI, 628. 
Tables, air, properties of, 477. 

coal classification, old, 457. 

Parr's, 458. 
sizes, 465, 466. 
coal, ultimate analyses, 460. 
combustion data, 473. 
compression pressures, 419. 
conductivities, 628. 
diagram factors, 325. 
draft through boilers, 578. 
eflEiciencies, steam engine, 358. 

Otto engine, 443. 
flue gas constants, 479, 481. 
formulas, volume changes of gases, 

S8. 
gas constants, 40. 
cycles, 102. 
expansions, 58. 
hydrocarbons, 491. 
logarithms, Appendix, 
natural gas, 470. 
Parr's classification (coal), 458. 
performance, steam eng., 355, 358. 

turbines, 395. 
pressure drops, flue gas in boiler, 578. 
producer gas, 602. 
steam, saturated. Appendix. 

superheated. Appendix, 
steam pressures, usual, 241. 
symbols. Appendix, 
volume changes (gas), 58. 
(i +]oger) -f-r, 325- 
Tail pipe, 666. 

pump, 669. 
Tar extractor, 616. 

in producer, 607. 
Temperature, absolute, 30. 

control (producer), 603-605. 
from combustion, 482-485. 
head, mean, 639-649. 
range (comp. eng.), 331. 
vaporization, 105. 
Temperature-entropy, changes of , gases, 72. 
vapors, 118. 
chart, 138, 143, Ap- 
pendix. 
Tests {see Performance). 
Thermal equiHbrium, vapor and liquid, 109. 
Thermal value {see Calorific value). 
Thermodynamics, defined, xvi. 
Throttled steam, 211, 212. 



8io 



INDEX 



Thrust bearing (turbine), 389. 

maximum (comp. eng.), 332. 
Time element (cyl. condensation), 231. 
Timer (ignition), 436. 
Timing opening, 441. 

valves, 434. 
Transmission of heat {see Heat trans.) 
Traps, 697. 
Travel, valve, 273. 
Trip cut-off, 309. 
Triple effect (vacuum pan.), 650. 
True comparison of performance, 354. 
Try cocks, 560. 
Tubes (boiler) exposed, 549. 

replacing, 547, 548. 

submerged, 549. 
Tumlirz's equation, 137. 
Turbines {see Steam Turbine). 
Turbo-compressors, 729. 
Turf, 456. 
Turning effort, int. comb, eng., 420. 

uniformity of, 332. 



u, 107, 133, 140. 
Ultimate analysis (coal), 460. 
Uncombined hydrogen, 486. 
Underload, effect on water rate, 233, 
Unit of evaporation, 561. 

heat, I, 6. 

work, 180. 
Uptakes {see Flues). 
Upton's Curves (sp. ht.), 484, 485. 
U. S. coal fields, 458. 

V, 286, V, 32, V, 33. 133, 286. 
Vacuum, effect on steam eng., 235, 354. 

on turbine, 367, 394. 
Valve {see Valve types) . 
action, 274. 
balancing, 291. 
definition, 272-273, 
diagrams, 274-288. {See Valve gear 

diagrams.) 
events, 274. 
fluttering, 721. 
friction, 291. 

gears, 271-322. (5ee Valve gears.) 
lead, 276. 
limitations, 288. 
opening, 273, 285-287, 295. 
steam velocity through, 286. 
travel, 273. 

types {see Valve types) . 
Valve gears, Allan Unk gear, 316. 
Buckeye, 302. 
cam, 322. 

CorUss, H. S., 293, 308. 
L. S., 307-314- 
crossed rod, 315. 



Valve gears, diagrams {see Valve gear dia- 
grams), 
double eccentric Corliss, 313. 
floating lever, 322. 
Gooch, 316. 
high speed, 292, 293. 
independent cut-off, 297. 
int. comb, eng., 438-442. 
Joy, 319- 
link, 314-317. 
low speed, 307-314. 
Mclntosh-Seymour, 306. 
Marshall, 318. 
Meyer, 304. 
open rod, 315. 
oscillating, 307. 
poppett, 321. 
Porter- Allen, 317. 
radial, 317-321. 
riding cut-off, 297, 302-307. 
Russell, 304. 

single eccentric Corliss, 309. 
Stephenson, 314. 
trip cut-off, 309. 
Walschaert, 320. 
Valve gear diagrams, Bilgram, 280, 299. 

elhptical, 277, 299. 

oval, 285. 

polar, 275. 

rectilinear, 275. 

Sweet, 278, 299. 

valve openings, 278. 

Zeuner, 279, 285. 
Valve types, Allen, 289. 

auxihary air, 425. 

auxiUary ported, 289. 

balanced, 291. 

blow off, 560. 

carburetting, 424. 

cooled (gas), 439. 

CorUss, 308, 309. 

cut-off (riding), 297, 302-307. 

double ported, 289. 

D-valve, 271. 

exhaust, 439, 441. 

external, 273. 

gas, 431. 

gridiron, 306. 

inlet, 439, 441. 

automatic, 439. 
main, 297. 
marine, 289. 
mixing, 423, 431, 432. 
multiport, 289. 
mushroom, 438. 
oscillating, 307. 
overload, turbine, 366. 
pilot, 382. 
piston, 288. 
poppet, 321, 322, 438. 



INDEX 



8ii 



Valve types, proportioning (gas), 431. 
relief, 292. 

riding cut-off, 297, 302-307. 
safety, 560. 
sleeve, 438. 
slide, gas, 438. 
stop, 560. 
Sweet, 290. 
Trick, 289. 
trip cut-off, 309. 
Woodbury, 291. 
Van der Waal's equation, 123. 
Vapor, cycles, 161-179. 
defined, 103, 123. 
dry, 109. 
ether, 154. 
expansion, 114. 
formation, 103. 
heat, 108. 

properties, 111-115. 
region, 123. 
saturated, 109, in. 
superheated, in. 
table (discussion), 113. 
wet, 109. 
Vaporization, heat of, X06-108. 
Vaporizer (producer), 606. 
Velocity, absolute, 371. 
bucket, 360. 
chimney gases, 582. 
compounding, 380, 382. 
critical (nozzle), gas, 714. 

steam, 705. 
diagram (turbine), 360. 
flow, flue gas, 576. 
gas, 713- 
steam, 702. 
jet, 360, 373. 
piston, 246, 286. 
relative, 371. 
steam through ports, 286. 
Volatile matter (coal), 456, 459, 506-510. 
Volume changes, gas, 53, 58. 

vapors, 146-160. 
Volumes, gases {see Gas constants). 

gas (from comb, of C), 477-482. 
steam, saturated, 133, Appendix, 
superheated, 137, Appen- 
dix, 
water, 113. 

Water, condensing, 20, 672-674. 
column, 560. 
curve, 138. 
gauge, 560. 

injection (air comp.), 725. 
jacket, 40s, 407, 72s. 



Water, legs, 555 • 

purification, 685-689. 
rate {see Water rate), 
seal, turbine, 379. 

producer, 612. 
specific heat, 130. 
treatment, 685-689. 
volume, 113. 
Water rate, 224. 

steam eng., 198, 201, 355, 358. 
steam turbine, 363, 391, 393- 
395- 
Water rate curves, steam engine, 232. 

turbine, 363, 365, 392. 
Weight, air, 477. 

flue gas, 495, 497-499. SOI. 
gases {see Gas constants). 
See Air for combustion. 
See Oxygen for combustion. 
Wet vacuum air pump, 678. 
Wet vapor method (producer), 605. 
Wetness factor, 206. 
Whistle, sentinel, 560. 
Willans' law, 352. 
Windage, 365. 

loss, 370. 
Wiredrawing, 211. 
Wood (fuel), 467. 

Work, areas (positive and neg.), 46. 
positive and negative, 78-79. 
Work done on and by piston, 23. 

- area for, 47, 49, 74-79. 

Work, equalization (multi. exp. eng.), 332, 

335, 341, 342. 
Work durmg changes, adiabatics, gas, 51. 
vapor, 156. 
isobarics, gas, 45. 

vapor, 149, 151. 
isothermals, gas, 48. 

vapor, 151. 
isovolumics, gas, 47. 
Work of cycles, Brayton (Joule), 99. 
Carnot, gas, 79-82. 

vapor, 162, 165. 
Clausius, 169, 172. 
Diesel, loi. 
Ericsson, 93. 

Otto (Beau de Rochas), 95. 
Rankine, 175, 176. 
rectangular PV, 178, 179. 
Stirling, 92. 
Working substance, 76, 397, 403. 

X, no. 

Zero, absolute, 30. 



SHORT-TITLE CATALOGUE 

OF THE 

PUBLICATIONS 

OF 

JOHN WILEY & SONS 

NEW YORK 

London: CHAPMAN & HALL, Limited 
Montreal, Can.: RENOUF PUB. CO. 



ARRANGED UNDER SUBJECTS 

Descriptive circulars sent on application. Books marked with an asterisk (*) are 
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Armsby — Principles of Animal Nutrition 8vo, $4 00 

Bowman — Forest Physiography 8vo, *5 00 

BuDD and Hansen — Arperican Horticultural Manual: 

Part I. Propagation, Culture, and Improvement 12mo, 1 50 

Part II. Systematic Pomology 12mo, 1 50 

Elliott — Engineering for Land Drainage 12mo, 2 00 

Practical Farm Drainage. (Second Edition, Rewritten) 12mo, 1 50 

Fuller — Domestic Water Supplies for the Farm 8vo, *1 50 

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Larsen and Whi'-e — Dairy Technology Small Svo, *1 50 

McKay and Lai jn — Principles and Practice of Butter-making Svo, *! 50 

Maynard — Lan ;ape Gardening as Applied to Home Decoration. . . 12mo, 1 50 
Record — Identi. jation of the Economic Woods of the United States.. .Svo, *1 25 
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Insects Injurious to Staple Crops 12mo, 1 50 

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Stockbridge — Rocks and Soils Svo, 2 50 

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Woll — Handbook for Farme; t and Dairymen 16mo, 1 50 

ARCHITECTURE. 

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Baldwin — Steam Heating for Buildings 12mo, 2 50 

Berg — Buildings and Structures of American Railroads 4to, 5 00 

1 



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Byrne — Inspection of Materials and Workmanship Employed in Construc- 
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Freitag — Architectural Engineering Svo, 3 50 

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Gerhard — Guide to Sanitary Inspections 12mo, 1 50 

Modern Baths and Bath Houses Svo, *3 00 

Sanitation of Public Buildings 12mo, 1 50 

Theatre Fires and Panics 12mo, 1 50 

The Water Supply, Sewerage and Plumbing of Modern City Buildings, 

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Greene — Elements of Heating and Ventilation Svo, *2 50 

Johnson — Statics by Algebraic and Graphic Methods Svo, 2 00 

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Peabody — Naval Architecture Svo, 7 50 

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Snow — Principal Species of Wood Svo, 3 50 

Wait — Engineering and Architectural Jurisprudence Svo, 6 00 

Sheep, 6 50 

Law of Contracts Svo, 3 00 

Law of Operations Preliminary to Construction in Engineering and 

Architecture Svo, 5 00 

Sheep, 5 50 

Wilson — Air Conditioning 12mo, 1 50 

Worcester and Atkinson — Small Hospitals, Establishment and Mainte- 
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Hospital 12mo, 1 25 



ASSAYING. 

Betts — Lead Refining by Electrolysis Svo, 4 00 

Fletcher — Practical Instructions in Quantitative Assaying with the Blow- 
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FuRMAN and Pardoe — Manual of Practical Assaying Svo, 3 00 

Lodge — Notes on Assaying and Metallurgical Laboratory Experiments. Svo, 3 00 

Low — Technical Methods of Ore Analysis Svo, 3 00 

Miller— Cyanide Process 12mo, 1 00 

Manual of Assaying 12mo, 1 00 

Minet — Production of Aluminum and its Industrial Use. (Waldo). . 12mo, 2 50 
Price and Meade — The Technical Analysis of Brass and the Non-Ferrous 

Alloys 12mo, *2 00 

Ricketts and Miller — Notes on Assaying Svo, 3 00 

Robine and Lenglen— Cyanide Industry. (Le Clerc.) Svo, 4 00 

Seamon — Manual for Assayers and Chemists Small Svo, *2 50 

2 



Ulke — Modern Electrolytic Copper Refining 8vo, S3 00 

Wilson — Chlorination Process 12mo, 1 50 

Cyanide Processes 12mo, 1 50 



ASTRONOMY. 

CoMSTOCK — Field Astronomy for Engineers 8vo, 2 50 

Craig — Azimuth 4to, 3 50 

Crandall — -Text-book on Geodesy and Least Squares 8vo, 3 00 

DooLiTTLE — -Treatise on Practical Astronomy Svo, 4 00 

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HosMER — Azimuth 16mo, mor., 1 00 

Text -book on Practical Astronomy Svo, *2 00 

Merriman — Elements of Precise Surveying and Geodesy Svo, 2 50 

MiCHiE and Harlow — Practical Astronomy Svo, *3 00 

Rust — Ex-meridian Altitude, Azimuth and Star-Finding Tables Svo, 5 00 

White — Elements of Theoretical and Descriptive Astronomy 12mo, *2 00 



BIOLOGY. 

CoHNHElM — Enzymes 12mo, *1 50 

Davenport — Statistical Methods with Special Reference to Biological 

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Effront and Prescott — Enzymes and Their Applications Svo, 3 00 

EuLER and Pope — General Chemistry of the Enzymes Svo, *3 00 

Mast — Light and Behavior of Organisms Svo, *2 50 

Prescott and Winslow — Elements of Water Bacteriology, with Special 

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Ward and Whipple — Freshwater Biology {In Press.) 

Whipple — -The Microscopy of Drinking Water Svo, 3 50 

Winslow — The Systematic Relationship of the Coccacese Small Svo, 2 50 



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Abderhalden — Physiological Chemistry in Thirty Lectures. (Hall and 

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Abegg — Theory of Electrolytic Dissociation, (von Ende.) 12mo, *1 25 

Alexeyeff — General Principles of Organic Syntheses. (Matthews.). . Svo, '3 00 
Allen — E.xercises in General Chemistry, Loose Leaf Laboratory Manual. 

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Tables for Iron Analysis Svo, 3 00 

Armsby — Principles of Animal Nutrition Svo, 4 00 

Arnold — Compendium of Chemistry. (Mandel.) Small Svo, 3 50 

Association of State and National Food and Dairy Departments, 

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Jamestown Meeting, 1907 Svo, 3 00 

Austen — Notes for Chemical Students 12mo, 1 50 

Bernadou — Smokeless Powder. — Nitro-cellulose, and Theory of the Cellu- 
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BiLTZ — Introduction to Inorganic Chemistry. (Hall and Phelan.).. 12mo, *1 25 
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Bingham and White — Laboratory Manual of Inorganic Chemistry. . . . 12mo, *1 00 

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Browne — Handbook of Sugar Analysis Svo, *6 00 

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Browning — Introduction to the Rarer Elements Svo, *1 50 

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Classen — Quantitative Analysis by Electrolysis. (Hall.) {In Press.) 

3 



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Cooper — Constitutional Analysis by Physico-chemical Methods (Inorganic), 

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Danneel — Electrochemistry. (Merriam.) 12mo, *1 25 

Dannerth — Methods of Textile Chemistry 12mo, 2 00 

DuHEM — Thermodynamics and Chemistry. (Burgess.) 8vo, 4 00 

EissLER — Modern High Explosives 8vo, 4 00 

Ekeley — Laboratory Manual of Inorganic Chemistry 12mo, *1 00 

Fletcher — Practical Instructions in Quantitative Assaying with the Blow- 
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Fowler- — ^Sewage Works Analyses 12mo, 2 00 

Fresenius — Manual of Qualitative Chemical Analysis. (Wells.) 8vo, 5 00 

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Fuertes — Water and Public Health 12mo, 1 50 

Fuller — Qualitative Analysis of Medicinal Preparations 12mo, *1 50 

FuRMAN and Pardoe — Manual of Practical Assaying.. 8vo, 3 00 

Getman — Exercises in Physical Chemistry 12mo, *2 00 

Gill — Gas and Fuel Analysis for Engineers 12mo, 1 25 

GoocH — Methods in Chemical Analysis 8vo, *4 00 

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Grotenfelt — Principles of Modern Dairy Practice. (Woll.) 12mo, 2 00 

Groth — Introduction to Chemical Crystallography. (Marshall.).. . 12mo, 1 25 
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Hanausek — Microscopy of Technical Products. (Winton.) 8vo, 5 00 

Haskins — Organic Chemistry 12mo, *2 00 

Herrick — Denatured or Industrial Alcohol 8vo, *4 00 

Hinds — Inorganic Chemistry 8vo, 3 00 

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Text-book of Inorganic Chemistry. (Cooper.) 8vo, 2 50 

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HoLLEY — Analysis of Paint and Varnish Products Small, 8vo, *2 50 

Lead and Zinc Pigments Small 8vo, *3 00 

Hopkins — Oil-chemists' Handbook 8vo, 3 00 

Jackson — Directions for Laboratory Work in Physiological Chemistry. .8vo, 1 25 
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Landauer — Spectrum Analysis. (Tingle.) Svo, 3 00 

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Low — Technical Method of Ore Analysis Svo, 3 00 

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McKay and Larsen — Principles and Practice of Butter-making Svo, *1 50 

Maire — Modern Pigments and their Vehicles 12mo, 2 00 

Mandel — Handbook for Bio-chemical Laboratory 12mo, 1 50 

Martin — Laboratory Guide to Qualitative Analysis with the Blowpipe. 12mo, *0 60 
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Mathewson — First Principles of Chemical Theory Svo, *1 00 

Matthews — Laboratory Manual of Dyeing and Textile Chemistry Svo, 3 50 

Textile Fibres Svo, 4 00 

Meyer — Determination of Radicles in Carbon Compounds. (Tingle.) 

Third Edition 12mo, *1 25 

Miller — Cyanide Process 12mo, 1 00 

Manual of Assaying 12mo, 1 00 

4 



MiNET — Production of Aluminum and its Industrial Use. (Waldo.) . . 12mo, $2 50 
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MiXTER — Elementary Text-book of Chemistry 12mo, 1 50 

Morgan — Elements of Physical Chemistry ■. . 12mo, 3 GO 

Physical Chemistry for Electrical Engineers 12mo, *1*50 

Moore — Experiments in Organic Chemistry ; 12mo, *0 50 

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Morse — Calculations used in Cane-sugar Factories 16mo, mor., 1 50 

MuiR — History of Chemical Theories and Laws 8vo, *4 00 

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Nelson — Analysis of Drugs and Medicines 12mo, *3 00 

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Owen and Standage — Dyeing and Cleaning of Textile Fabrics 12mo, 2 00 

Palmer — Practical Test Book of Chemistry 12mo, *1 00 

Pauli — Physical Chemistry in the Service of Medicine. (Fischer.).. 12mo, *1 25 

PiCTET — Alkaloids and their Chemical Constitution. (Biddle.) 8vo, 5 00 

Prescott and Winslovv — Elements of Water Bacteriology, with Special 

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Reisig — Guide to Piece-Dyeing 8vo, *25 00 

Richards and Woodman — Air, Water, and Food from a Sanitary Stand- 
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RiCKETTS and Miller — Notes on Assaying 8vo, 3 00 

RiDEAL — Disinfection and the Preservation of Food 8vo, 4 00 

RiGGS — Elementary Manual for the Chemical Laboratory 8vo, 1 25 

Robine and Lenglen — Cyanide Industry. (Le Clerc.) 8vo, 4 00 

Ruddiman — Incompatibilities in Prescriptions Svo, 2 00 

Whys in Pharmacy 12mo, 1 00 

Ruer — Elements of Metallography. (Mathewson.) Svo, *3 00 

Sabin — Industrial and Artistic Technology of Paint and Varnish 8vo, 3 00 

Salkowski — Physiological and Pathological Chemistry. (Orndorff.) . . .8vo, 2 50 
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Seamon — Manual for Assayers and Chemists Small Svo, *2 50 

Smith — Lecture Notes on Chemistry for Dental Students Svo, *2 50 

Spencer — Handbook for Cane Sugar Manufacturers 16mo, mor., 3 00 

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Stockbridge — Rocks and Soils Svo, 2 50 

Stone — Practical Testing of Gas and Gas Meters Svo, 3 50 

Tillman — Descriptive General Chemistry Svo, *3 00 

Elementary Lessons in Heat Svo, *1 50 

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Turneaure and Russell — Public Water-supplies Svo, 5 00 

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Ward and Whipple — Freshwater Biology {In Press.) 

Ware — Beet-sugar Manufacture and Refining. Vol. I Svo, 4 00 

Vol. II Svo, 5 00 

Washington — Manual of the Chemical Analysis of Rocks Svo, 2 00 

Weaver — Military Explosives Svo, *3 00 

Wells — Laboratory Guide in Qualitative Chemical Analysis Svo, 1 50 

Short Course in Inorganic Qualitative Chemical Analysis for Engineering 

Students 12mo, 1 50 

Te.xt-book of Chemical Arithmetic 12mo, 1 25 

Whipple — Microscopy of Drinking-water Svo, 3 50 

Wilson — Chlorination Process 12mo, 1 50 

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Zsigmondy — Colloids and the Ultramicroscope. (Alexander.) .Large 12mo, 3 00 
5 



CIVIL ENQINEERINQ. 

BRIDGES AND ROOFS, HYDRAULICS, MATERIALS OF ENGINEER- 
ING. RAILWAY ENGINEERING. 

American Civil Engineers' Pocket Book. (Mansfield Merriman, 

Editor-in-chief.) 16mo, moT.*$5 00 

Baker — Engineers' Surveying Instruments 12mo, 3 00 

BlXBY — Graphical Computing Table Paper 19| X24i inches, 25 

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CoMSTOCK — Field Astronomy for Engineers 8vo, 2 50 

CoRTHELL — Allowable Pressure on Deep Foundations 12mo, *1 25 

Crandall — Text-book on Geodesy and Least Squares 8vo, 3 00 

Davis — Elevation and Stadia Tables 8vo, 1 00 

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Hauch and Rice — Tables of Quantities for Preliminary Estimates . . . 12mo, *1 25 

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Ives and Hilts — Problems in Surveying, Railroad Surveying and Geod- 
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Nugent — Plane Surveying Svo, 3 50 

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Ogden and Cleveland — Practical Methods of Sewage Disposal for Resi- 
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Parsons — Disposal of Municipal Refuse Svo, 2 00 

Patton — Treatise on Civil Engineering Svo, half leather, 7 50 

Reed — Topographical Drawing and Sketching 4to, 5 00 

RiEMER — Shaft-sinking under Difficult Conditions. (Corning and Peele.) 

Svo, 

Siebert and Biggin — Modern Stone-cutting and Masonry Svo, 

Smith — Manual of Topographical Drawing. (McMillan.) Svo, 

Soper — Air and Ventilation of Subways 12mo, 

Tracy — Exercises in Surveying 12mo, mor.. 

Plane Surveying 16mo, mor., 

Venable — Garbage Crematories in America Svo, 

Methods and Devices for Bacterial Treatment of Sewage Svo, 

Wait — Engineering and Architectural Jurisprudence Svo, 

Sheep, 

Law of Contracts Svo, 

Law of Operations Preliminary to Construction in Engineering and 

Architecture Svo, 

Sheep, 

Warren — Stereotomy — Problems in Stone-cutting Svo, 

Waterbury — Vest-Pocket Hand-book of Mathematics for Engineers. 

2i X5| inches, mor., *1 00 

Enlarged Edition, Including Tables mor., *1 50 

Webb — Problems in the Use and Adjustment of Engineering Instruments. 

16mo, mor., 1 25 
Wilson — Topographic, Trigonometric and Geodetic Surveying Svo, 3 50 

6 



3 


00 


1 


50 


2 


50 


2 


50 


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00 


3 


00 


2 


00 


3 


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6 


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BRIDGES AND ROOFS. 

Bishop — Structural Details of Hip and Valley Rafters . . . Oblong large 8vo. *$1 75 
BoLLER — Practical Treatise on the Construction of Iron Highway Bridges 

8vo, 2 00 

Thames River Bridge Oblong paper, *5 00 

Burr and Falk — Design and Construction of Metallic Bridges Svo, 5 00 

Influence Lines for Bridge and Roof Comp-atations Svo, 3 00 

Du Bois — Mechanics of Engineering. Vol. II Small 4to. 10 00 

Foster — Treatise on Wooden Trestle Bridges 4to, 5 00 

Fowler — Ordinary Foundations Svo, 3 50 

Greene — Arches in Wood, Iron, and Stone Svo, 2 50 

Bridge Trusses Svo, 2 50 

Roof Trusses Svo, 1 25 

Grimm — Secondary Stresses in Bridge Trusses Svo, 2 50 

Heller — Stresses in Structures and the Accompanying Deformations. .Svo, 3 00 

Howe — Design of Simple Roof-trusses in Wood and Steel Svo, 2 00 

Symmetrical Masonry Arches Svo, 2 50 

Treatise on Arches Svo, 4 00 

Hudson — Deflections and Statically Indeterminate Stresses Small 4to, *3 50 

Plate Girder Design Svo, *1 50 

Jacoby — Structural Details, or Elements of Design in Heavy Framing, Svo, *2 25 
Johnson, Bryan and Turneaure — Theory and Practice in the Designing of 
Modern Framed Structures. New Edition. 

Part I. Stresses in Simple Structures Svo, *3 00 

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Merriman and Jacoby — Text-book on Roofs and Bridges: 

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Part II. Graphic Statics Svo, 2 50 

Part III. Bridge Design Svo, 2 50 

Part IV. Higher Structures Svo, 2 50 

Richer — Design and Construction of Roofs Svo, 5 00 

Sondericker — Graphic Statics, with Applications to Trusses, Beams, and 

Arches •. Svo, *2 00 

Waddell — De Pontibus, Pocket-book for Bridge Engineers. . . .16mo, mor., 2 00 
Specifications for Steel Bridges 12mo, *0 50 

HYDRAULICS. 

Barnes — Ice Formation Svo, 3 00 

Bazin — ^Experiments upon the Contraction of the Liquid Vein Issuing from 

an Orifice. (Trautwine.) Svo, 2 00 

Bovey — Treatise on Hydraulics Svo, 5 00 

Church — Diagrams of Mean Velocity of Water in Open Channels. 

Oblong 4to, paper, 1 50 

Hydraulic Motors . Svo, 2 00 

Mechanics of Fluids (Being Part IV of Mechanics of Engineering) . .Svo, 3 00 

Coffin — Graphical Solution' of Hydraulic Problems 16mo, mor., 2 50 

Flather — Dynamometers, and the Measurement of Power 12mo, 3 00 

FoLWELL — Water-supply Engineering Svo, 4 00 

Frizell — Water-power Svo, 5 00 

FuERTES — Water and Public Health 12mo, 1 50 

Fuller — Domestic Water Supplies for the Farm Svo, *1 50 

Ganguillet and Kutter — General Formula for the Uniform Flow of Water 

in Rivers and Other Channels. (Hering and Trautwine.).. .Svo, 4 00 

Hazen — Clean Water and How to Get It Small Svo, 1 50 

Filtration of Public Water-supplies Svo, 3 00 

Hazelhurst — Towers and Tanks for Water-works Svo, 2 50 

Herschel — 115 Experiments on the Carrying Capacity of Large, Riveted, 

Metal Conduits ' Svo, 2 00 

Hoyt and Grover — River Discharge Svo, 2 00 

Hubbard and Kiersted — Water-works Management and Maintenance, Svo, 4 00 
Lyndon — Development and Electrical Distribution of Water Power. .Svo, *3 00 
Mason — Water-supply. (Considered Principally from a Sanitary Stand- 
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Merriman — Elements of Hydraulics 12mo, *1 00 

Treatise on Hydraulics. 9th Edition, Rewritten Svo, *4 00 

7 



MoLiTOR — Hydraulics of Rivers, Weirs and Sluices 8vo,*|2 00 

Morrison and Brodie — High Masonry Dam Design 8vo, *1 50 

Schuyler — Reservoirs for Irrigation, Water-power, and Domestic Water 

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Thomas and Watt — Improvement of Rivers 4to, *6 00 

TuRNEAURE and Russell — Public Water-supplies 8vo, 5 00 

Wegmann — Design and Construction of Dams. 6th Ed., enlarged 4to, *6 00 

Water Supply of the City of New York from 1658 to 1895 4to, 10 00 

Whipple — Value of Pure Water Small 8vo, 1 00 

Williams and Hazen — Hydraulic Tables 8vo, 1 50 

Wilson — Irrigation Engineering 8vo, 4 00 

Wood— Turbines 8vo, 2 50 

MATERIALS OP ENGINEERING. 

Baker — Roads and Pavements 8vo, 5 00 

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3 00 
6 00 


4 50 
3 00 


7l50 


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*3 00 



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10 



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11 



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Svo, *4 00 

13 



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MacCord — Kinematics; or, Practical Mechanism 8vo, $5 00 

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14 



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Waterbury — Laboratory Manual for Testing Materials of Construction. 

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Wood (De V.) — Elements of Analytical Mechanics Svo, 3 00 

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STEAM-ENGINES AND BOILERS. 

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Chase — Art of Pattern Making 12mo, 2 50 

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Kneass — Practice and Theory of the Injector Svo, 1 50 

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Miller, Berry, and Riley — Problems in Thermodynamics.. . .Svo, paper, 75 

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REAG.A.N — Locomotives: Simple, Compound, and Electric. New Edition. 

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Spangler — Notes on Thermodynamics 12mo, 1 00 

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Greene, and Marshall — Elements of Steam-engineering Svo, 3 00 

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Part I. History, Structure, and Theory Svo, 6 00 

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